(* ::Package:: *)

(* ::Title:: *)
(*SUSYHD v1.0.2*)


(* ::Text:: *)
(*This package computes the pole mass of the Higgs boson in the MSSM using the effective field theory technique. *)
(*For the details of the calculation and conventions please refer to the file of documentation and examples SUSYHD_Examples.nb or the paper arXiv:1504.05200*)


(* ::Section::Closed:: *)
(*Preambula*)


BeginPackage["SUSYHD`"]


(*uncomment this cell if you need the values of the MSSM bottom and tau Yukawa couplings in the Overscript[DR, _] scheme*)
(*gbMSSM::usage="gbMSSM[Q,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]";
gtauMSSM::usage="gtauMSSM[Q,mL3,mE3,M2,M1,\[Mu],tan\[Beta]]";*)


Print["----------------------------------
SUSYHD v1.0.2 (2015)
Javier Pardo Vega and Giovanni Villadoro
http://www.ictp.it/~susyhd
----------------------------------"];
MHiggs::usage="MHiggs[parameterslist] computes the pole mass of the Higgs boson (in units of GeV) as a function of the supersymmetric parameters in the \!\(\*OverscriptBox[\(DR\), \(_\)]\) scheme evaluated at the scale Q=\!\(\*
StyleBox[SqrtBox[
RowBox[{SubscriptBox[\"m\", SubscriptBox[\"Q\", \"3\"]], SubscriptBox[\"m\", SubscriptBox[\"U\", \"3\"]]}]],\nFontSize->10]\). 

The input \!\(\*
StyleBox[\"parameterslist\",\nFontSlant->\"Italic\"]\) should be a list of the following form:
	{tan\[Beta],\!\(\*SubscriptBox[\(M\), \(1\)]\),\!\(\*SubscriptBox[\(M\), \(2\)]\),\!\(\*SubscriptBox[\(M\), \(3\)]\),\[Mu],\!\(\*SubscriptBox[\(A\), \(t\)]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), \(A\)]\)}.

It also accepts shorter lists and assign suitable values for the parameters that are not input:
	{tan\[Beta],m0}: assumes degenerate SUSY masses m0 and \!\(\*SubscriptBox[\(A\), \(t\)]\)=m0
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\)}: like before but with generic \!\(\*SubscriptBox[\(A\), \(t\)]\)
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\),m12}: like before but with generic fermion masses \!\(\*SubscriptBox[\(M\), \(1\)]\)=\!\(\*SubscriptBox[\(M\), \(2\)]\)=\!\(\*SubscriptBox[\(M\), \(3\)]\)=\[Mu]=m12 
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\),m12,\[Mu]}: like before but with generic \[Mu]
	{tan\[Beta],\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(A\), \(t\)]\),m12,\[Mu]}: like before but with \!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\)\[NotEqual]\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\), the other scalar masses are m0=\!\(\*
StyleBox[SqrtBox[
RowBox[{SubscriptBox[\"m\", SubscriptBox[\"Q\", \"3\"]], SubscriptBox[\"m\", SubscriptBox[\"U\", \"3\"]]}]],\nFontSize->10]\)
	{tan\[Beta],\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(A\), \(t\)]\),\!\(\*SubscriptBox[\(M\), \(1\)]\),\!\(\*SubscriptBox[\(M\), \(2\)]\),\!\(\*SubscriptBox[\(M\), \(3\)]\),\[Mu]}: like before but with generic gaugino masses.";
MHiggs::warning="We recommend to choose the renormalization scale \!\(\*SubscriptBox[\(m\), \(SUSY\)]\) near the stop average mass (\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\)\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\)\!\(\*SuperscriptBox[\()\), \(1/2\)]\).";
MHiggs::warningsplit="The Split-SUSY calculation is suitable when the scalars are heavier than the gauginos and higgsinos. High-Scale calculation will be used.";
MHiggs::variables="One of the variables is not well-defined.";
MHiggs::negative="The Higgs mass squared is negative. The value 0 is returned.";
MHiggs::bottomYukawa="Bottom Yukawa is non-perturbative.";
MHiggs::tauYukawa="Tau Yukawa is non-perturbative.";
split::usage="split is an option for MHiggs. When activated (split\[Rule]True), the code uses the Split-SUSY effective theory to resum the logs between the fermion scale \!\(\*SubscriptBox[\(Q\), \(split\)]\)=max(\[Mu],\!\(\*SubscriptBox[\(M\), \(2\)]\)) and the SUSY scale. In this case the RGE are integrated numerically and the code is sensibly slower. In the whole range relevant for the Higgs mass the effect of this resummation is very small.
Default value: split\[Rule]False";
numerical::usage="\!\(\*
StyleBox[\"numerical\",\nFontSlant->\"Italic\"]\) is an option for MHiggs and \[CapitalDelta]MHiggs. When activated (numerical\[Rule]True) the program integrates the RGE numerically and is much slower. 
Default value: numerical\[Rule] False (recommended)";
hiOrd::usage="hiOrd is an option for MHiggs and \[CapitalDelta]MHiggs which controls what two-loop SUSY thresholds are included. It also determines if the \!\(\*OverscriptBox[\(MS\), \(_\)]\) running top Yukawa coupling is calculated at two or three loops from the pole mass of the top quark. This option has the form hiOrd->{t1,t2,t3,t4} where each component take values 0 (correction excluded) or 1 (correction included). Each component controls the following corrections:
t1: two-loop O(\!\(\*SubscriptBox[\(\[Alpha]\), \(t\)]\)\!\(\*SubscriptBox[\(\[Alpha]\), \(S\)]\)) SUSY threshold
t2: two-loop O(\!\(\*SubsuperscriptBox[\(\[Alpha]\), \(t\), \(2\)]\)) SUSY threshold
t3: one-loop O(\!\(\*SubscriptBox[\(\[Alpha]\), \(b, \[Tau]\)]\)) including tan\[Beta]-enhanced corrections.
t4: three-loop O(\!\(\*SubsuperscriptBox[\(\[Alpha]\), \(S\), \(3\)]\)) correction to the determination of the \!\(\*OverscriptBox[\(MS\), \(_\)]\) top Yukawa coupling
By default all corrections are included, i.e. hiOrd\[Rule]{1,1,1,1}.";
Rscale::usage="Rscale is an option for MHiggs and \[CapitalDelta]MHiggs that allows to change the scale at which the MSSM parameters are given as input. The program does not perform any RGE resummation of the soft parameters, it is thus recommended to use a scale close to the default one.
Default value: Rscale\[Rule]\!\(\*
StyleBox[SqrtBox[
RowBox[{SubscriptBox[\"m\", SubscriptBox[\"Q\", \"3\"]], SubscriptBox[\"m\", SubscriptBox[\"U\", \"3\"]]}]],\nFontSize->10]\)";
RscaleSplit::usage="\!\(\*
StyleBox[\"RscaleSplit\",\nFontSlant->\"Italic\"]\) is an option for MHiggs which allows to change the scale of the Split-SUSY effective theory. 
Default value: Rscale\[Rule]max(\[Mu],\!\(\*SubscriptBox[\(M\), \(2\)]\))";
scheme::usage="\!\(\*
StyleBox[\"scheme\",\nFontSlant->\"Italic\"]\) is an option for MHiggs and \[CapitalDelta]MHiggs which allows to input the MSSM parameters in the on-shell scheme (scheme\[Rule]\"OS\").
Default value: scheme\[Rule]\"DRbar\" ";
SetSMparameters::usage="SetSMparameters[\!\(\*SubscriptBox[\(m\), \(t\)]\)\!\(\*
StyleBox[\",\",\nFontSlant->\"Italic\"]\)\!\(\*SubscriptBox[\(\[Alpha]\), \(S\)]\)(\!\(\*SubscriptBox[\(m\), \(Z\)]\))] sets the input values for the OS top mass \!\(\*SubscriptBox[\(m\), \(t\)]\) and the strong coupling at the scale of the mass of the Z-boson \!\(\*SubscriptBox[\(\[Alpha]\), \(S\)]\)(\!\(\*SubscriptBox[\(M\), \(Z\)]\)). The default values are \!\(\*SubscriptBox[\(m\), \(t\)]\)=173.34 GeV and \!\(\*SubscriptBox[\(\[Alpha]\), \(S\)]\)(\!\(\*SubscriptBox[\(m\), \(Z\)]\))=0.1185.";
useMStopYukawa::usage="useMStopYukawa is an option for SetSMparameters which allows to input the \!\(\*OverscriptBox[\(MS\), \(_\)]\) top Yukawa coupling \!\(\*SubsuperscriptBox[\(y\), \(t\), OverscriptBox[\(MS\), \(_\)]]\)(\!\(\*SubscriptBox[\(m\), \(t\)]\)) in place of the pole mass of the top quark (useMStopYukawa\[Rule]True).
Default value: useMStopYukawa\[Rule]False.";
\[CapitalDelta]MHiggs::usage="\!\(\*
StyleBox[\"\[CapitalDelta]MHiggs\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\"[\",\nFontSlant->\"Italic\"]\)parameterslist\!\(\*
StyleBox[\"]\",\nFontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",\nFontSlant->\"Italic\"]\)estimates the theoretical uncertainty in the calculation of the Higgs mass (in units of GeV). 

The input \!\(\*
StyleBox[\"parameterslist\",\nFontSlant->\"Italic\"]\) should be a list of the following form:
	{tan\[Beta],\!\(\*SubscriptBox[\(M\), \(1\)]\),\!\(\*SubscriptBox[\(M\), \(2\)]\),\!\(\*SubscriptBox[\(M\), \(3\)]\),\[Mu],\!\(\*SubscriptBox[\(A\), \(t\)]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(D\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(2\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(L\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(E\), \(1\)]]\),\!\(\*SubscriptBox[\(m\), \(A\)]\)}.

It also accepts shorter lists and assign suitable values for the parameters that are not input:
	{tan\[Beta],m0}: assumes degenerate SUSY masses m0 and \!\(\*SubscriptBox[\(A\), \(t\)]\)=m0
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\)}: like before but with generic \!\(\*SubscriptBox[\(A\), \(t\)]\)
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\),m12}: like before but with generic fermion masses \!\(\*SubscriptBox[\(M\), \(1\)]\)=\!\(\*SubscriptBox[\(M\), \(2\)]\)=\!\(\*SubscriptBox[\(M\), \(3\)]\)=\[Mu]=m12 
	{tan\[Beta],m0,\!\(\*SubscriptBox[\(A\), \(t\)]\),m12,\[Mu]}: like before but with generic \[Mu]
	{tan\[Beta],\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(A\), \(t\)]\),m12,\[Mu]}: like before but with \!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\)\[NotEqual]\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\), the other scalar masses are m0=\!\(\*
StyleBox[SqrtBox[
RowBox[{SubscriptBox[\"m\", SubscriptBox[\"Q\", \"3\"]], SubscriptBox[\"m\", SubscriptBox[\"U\", \"3\"]]}]],\nFontSize->10]\)
	{tan\[Beta],\!\(\*SubscriptBox[\(m\), SubscriptBox[\(Q\), \(3\)]]\),\!\(\*SubscriptBox[\(m\), SubscriptBox[\(U\), \(3\)]]\),\!\(\*SubscriptBox[\(A\), \(t\)]\),\!\(\*SubscriptBox[\(M\), \(1\)]\),\!\(\*SubscriptBox[\(M\), \(2\)]\),\!\(\*SubscriptBox[\(M\), \(3\)]\),\[Mu]}: like before but with generic gaugino masses.";
\[CapitalDelta]MHiggs::tachyon="The stops become tachyonic when varying the renormalization scale. A large uncertainty in the Higgs mass using the effective field theory in the \!\(\*OverscriptBox[\(DR\), \(_\)]\) scheme is expected.";
sources::usage="\!\(\*
StyleBox[\"sources\",\nFontSlant->\"Italic\"]\) is an option for \[CapitalDelta]MHiggs. It selects which sources of theoretical uncertainties of the Higgs mass calculation are included.This option has the form sources\[Rule]{t1,t2,t3} where each component take values 0 (source excluded) or 1 (source included). Each component controls the following source of uncertainty:
t1: SM: from higher-order corrections in the SM thresholds and RGE
t2: SUSY: from missing threshold corrections at the SUSY scale
t3: EFT: from higher order correction in the effective field theory expansion.
By default all sources are included: sources\[Rule]{1,1,1}.
The total is taken as the linear sum.";
solutionSMRGEs::usage="solution of the three-loop SM renormalization group equations.";
(********)
(********)
(*MhpoleHSS::usage="MhpoleHSS[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] computes the pole mass of the Higgs in High-Scale-SUSY as a function of the supersymmetric parameters in the Overscript[DR, _] scheme.";
(*MhpoleHSS::warning="We recommend to choose the renormalization scale Overscript[m, ~] near the stop average mass (Subscript[m, Subscript[Q, 3]]Subscript[m, Subscript[U, 3]])^(1/2).";*)
MhpoleHSSfast::usage="MhpoleHSSfast[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] computes the pole mass of the Higgs in High-Scale-SUSY as a function of the supersymmetric parameters in the Overscript[DR, _] scheme. It is an optimized version of MhpoleHSS.";
(*MhpoleHSSfast::warning="We recommend to choose the renormalization scale Overscript[m, ~] near the stop average mass (Subscript[m, Subscript[Q, 3]]Subscript[m, Subscript[U, 3]])^(1/2).";*)
MhpoleSplit::usage="MhpoleSplit[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] computes the pole mass of the Higgs in Split Supersymmetry as a function of the supersymmetric parameters in the Overscript[DR, _] scheme.";
\[CapitalDelta]MhpoleHSSmom::usage="\[CapitalDelta]MhpoleHSSmom[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the uncertainty in the Higgs mass due to effects v^2/Overscript[m, ~]^2-suppressed.";
\[CapitalDelta]MhpoleHSSSM::usage="\[CapitalDelta]MhpoleHSSSM[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the uncertainty in the Higgs mass due to missing SM corrections in the the RGEs and the matching at the EW scale.";
\[CapitalDelta]MhpoleHSSQ::usage="\[CapitalDelta]MhpoleHSSQ[n,Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] calculates the shift in the Higgs mass induced by changing the renormalization scale by a factor n around the SUSY scale. It depends on the two-loop threshold corrections that are included in the calculation through the option hiOrd->{t1,t2,t3,t4}.";
\[CapitalDelta]MhpoleHSSbottom::usage="\[CapitalDelta]MhpoleHSSbottom[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] calculates the shift in the Higgs mass produced by the resummation of the tan\[Beta]-enhanced contributions.";
MhpoleHSSUnc::usage="\[CapitalDelta]MhpoleHSSUnc[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the total uncertainty in the calculation of the Higgs mass.";
\[CapitalDelta]MhpoleHSSmomfast::usage="\[CapitalDelta]MhpoleHSSmomfast[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the uncertainty in the Higgs mass due to effects v^2/Overscript[m, ~]^2-suppressed.(fast version)";
\[CapitalDelta]MhpoleHSSSMfast::usage="\[CapitalDelta]MhpoleHSSSMfast[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the uncertainty in the Higgs mass due to missing SM corrections in the the RGEs and the matching at the EW scale.(fast version)";
\[CapitalDelta]MhpoleHSSQfast::usage="\[CapitalDelta]MhpoleHSSQfast[n,Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] calculates the shift in the Higgs mass induced by changing the renormalization scale by a factor n around the SUSY scale. It depends on the two-loop threshold corrections that are included in the calculation thorugh the option hiOrd->{t1,t2,t3,t4}.(fast version)";
\[CapitalDelta]MhpoleHSSbottomfast::usage="\[CapitalDelta]MhpoleHSSbottomfast[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] calculates the shift in the Higgs mass produced by the resummation of the tan\[Beta]-enhanced contributions.(fast version)";
MhpoleHSSUncfast::usage="\[CapitalDelta]MhpoleHSSUncfast[Overscript[m, ~],Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],tan\[Beta],Subscript[X, t]] estimates the total uncertainty in the calculation of the Higgs mass.(fast version)";*)


Begin["Private`"]


(* ::Title::Closed:: *)
(*SM RGEs*)


(* ::Text:: *)
(*This sub-package solves the renormalization group equations of the Standard Model up to the three loop order. *)


(* ::Section::Closed:: *)
(*Preambula*)


(*SM\[Beta]::usage="SM\[Beta][loops,coupling] gives the SM \[Beta]-function of a coupling up to a given order specified by loops";
SMrun::usage="SMrun[variables,initialconds,tmin,tmax,opts] solves the coupled RGEs of the variables with the initial coditions given by initialconds between tmin and tmax. 
 It accepts the options of NDSolve. For time saving we recommend the optsrun";
optsSMrun::usage="Default options for the function SMrun. It selects the numerical method used by NDSolve and the precision goal";
{Subscript[g, 1],g1,Subscript[g, 2],g2,Subscript[g, 3],g3,Subscript[g, t],gt,Subscript[g, \[Tau]],g\[Tau],Subscript[g, b],gb,\[Lambda]};(*The names of the couplings are not encapsulated.*)*)


(* ::Section::Closed:: *)
(*Manipuation : rationalization of the three loop beta functions*)


(* ::Input:: *)
(*(*Here we rationalize the numbers in the three loop beta functions*)*)
(*SM\[Beta]aux[3,\[Lambda]]:=(\[Lambda]^3 (6011.35` \[Lambda]+873 Subscript[g, t]^2-387.452` Subscript[g, 2]^2-77.49` Subscript[g, 1]^2)+\[Lambda]^2 Subscript[g, t]^2 (1768.26` Subscript[g, t]^2+160.77` Subscript[g, 3]^2-359.539` Subscript[g, 2]^2-63.869` Subscript[g, 1]^2)+\[Lambda]^2 (-790.28` Subscript[g, 2]^4-185.532` Subscript[g, 1]^4-316.64` Subscript[g, 2]^2 Subscript[g, 1]^2)+\[Lambda] Subscript[g, t]^4 (-223.382` Subscript[g, t]^2-662.866` Subscript[g, 3]^2-5.47` Subscript[g, 2]^2-21.015` Subscript[g, 1]^2)+\[Lambda] Subscript[g, t]^2 (356.968` Subscript[g, 3]^4-319.664` Subscript[g, 2]^4-74.8599` Subscript[g, 1]^4+15.1443` Subscript[g, 3]^2 Subscript[g, 2]^2+17.454` Subscript[g, 3]^2 Subscript[g, 1]^2+5.615` Subscript[g, 2]^2 Subscript[g, 1]^2)+\[Lambda] Subscript[g, 2]^4 (-57.144` Subscript[g, 3]^2+865.483` Subscript[g, 2]^2+79.638` Subscript[g, 1]^2)+\[Lambda] Subscript[g, 1]^4 (-8.381` Subscript[g, 3]^2+61.753` Subscript[g, 2]^2+28.168` Subscript[g, 1]^2)+Subscript[g, t]^6 (-243.149` Subscript[g, t]^2+250.494` Subscript[g, 3]^2+74.138` Subscript[g, 2]^2+33.93` Subscript[g, 1]^2)+Subscript[g, t]^4 (-50.201` Subscript[g, 3]^4+15.884` Subscript[g, 2]^4+15.948` Subscript[g, 1]^4+13.349` Subscript[g, 3]^2 Subscript[g, 2]^2+17.57` Subscript[g, 3]^2 Subscript[g, 1]^2-70.356` Subscript[g, 2]^2 Subscript[g, 1]^2)+Subscript[g, t]^2 Subscript[g, 3]^2 (16.464` Subscript[g, 2]^4+1.016` Subscript[g, 1]^4+11.386` Subscript[g, 2]^2 Subscript[g, 1]^2)+Subscript[g, t]^2 Subscript[g, 2]^4 (62.5` Subscript[g, 2]^2+13.041` Subscript[g, 1]^2)+Subscript[g, t]^2 Subscript[g, 1]^4 (10.627` Subscript[g, 2]^2+11.117` Subscript[g, 1]^2)+Subscript[g, 3]^2 (7.536` Subscript[g, 2]^6+0.663` Subscript[g, 1]^6+1.507` Subscript[g, 2]^4 Subscript[g, 1]^2+1.105` Subscript[g, 2]^2 Subscript[g, 1]^4)-114.091` Subscript[g, 2]^8-1.508` Subscript[g, 1]^8-37.889` Subscript[g, 2]^6 Subscript[g, 1]^2+6.5` Subscript[g, 2]^4 Subscript[g, 1]^4-1.543` Subscript[g, 2]^2 Subscript[g, 1]^6);*)
(*SM\[Beta]aux[3,Subscript[g, t]]:=Subscript[g, t]^2 (Subscript[g, t]^4 (58.6028` Subscript[g, t]^2+198 \[Lambda]-157 Subscript[g, 3]^2-1593/16 Subscript[g, 2]^2-2437/80 Subscript[g, 1]^2)+\[Lambda] Subscript[g, t]^2 ((15 \[Lambda])/4+16 Subscript[g, 3]^2-135/2 Subscript[g, 2]^2-127/10 Subscript[g, 1]^2)+Subscript[g, t]^2 (363.764` Subscript[g, 3]^4+16.99` Subscript[g, 2]^4-24.422` Subscript[g, 1]^4+48.37` Subscript[g, 3]^2 Subscript[g, 2]^2+18.074` Subscript[g, 3]^2 Subscript[g, 1]^2+34.829` Subscript[g, 2]^2 Subscript[g, 1]^2)+\[Lambda]^2 (-36 \[Lambda]+45 Subscript[g, 2]^2+9 Subscript[g, 1]^2)+\[Lambda] (-(1/16) (171 Subscript[g, 2]^4)-1089/400 Subscript[g, 1]^4+117/40 Subscript[g, 2]^2 Subscript[g, 1]^2)-619.35` Subscript[g, 3]^6+169.829` Subscript[g, 2]^6+16.099` Subscript[g, 1]^6+73.654` Subscript[g, 3]^4 Subscript[g, 2]^2-15.096` Subscript[g, 3]^4 Subscript[g, 1]^2-21.072` Subscript[g, 3]^2 Subscript[g, 2]^4-22.319` Subscript[g, 3]^2 Subscript[g, 1]^4-321/20 Subscript[g, 3]^2 Subscript[g, 2]^2 Subscript[g, 1]^2-4.743` Subscript[g, 2]^4 Subscript[g, 1]^2-4.442` Subscript[g, 2]^2 Subscript[g, 1]^4);*)
(*Rationalize[ -2472.28]*)
(*Rationalize[SM\[Beta]aux[3,\[Lambda]]]*)
(*Rationalize[SM\[Beta]aux[3,Subscript[g, t]]]*)


(* ::Section::Closed:: *)
(*Beta functions*)


With[{\[Kappa]=1/(4\[Pi])^2},
SM\[Beta][1,Subscript[g, 1]]:=\[Kappa] Subscript[g, 1]^4 (41/10);
SM\[Beta][2,Subscript[g, 1]]:=SM\[Beta][1,Subscript[g, 1]]+\[Kappa]^2 Subscript[g, 1]^4 (44/5 Subscript[g, 3]^2+27/10 Subscript[g, 2]^2+199/50 Subscript[g, 1]^2-17/10 Subscript[g, t]^2-1/2 Subscript[g, b]^2-3/2 Subscript[g, \[Tau]]^2);
SM\[Beta][3,Subscript[g, 1]]:=SM\[Beta][2,Subscript[g, 1]]+\[Kappa]^3 Subscript[g, 1]^4 (Subscript[g, t]^2 (189/16 Subscript[g, t]^2-29/5 Subscript[g, 3]^2-471/32 Subscript[g, 2]^2-2827/800 Subscript[g, 1]^2)+\[Lambda] (-( 9/5)\[Lambda]+9/10 Subscript[g, 2]^2+27/50 Subscript[g, 1]^2)+297/5 Subscript[g, 3]^4+789/64 Subscript[g, 2]^4-(388613 Subscript[g, 1]^4)/24000-3/5 Subscript[g, 3]^2 Subscript[g, 2]^2-137/75 Subscript[g, 3]^2 Subscript[g, 1]^2+123/160 Subscript[g, 2]^2 Subscript[g, 1]^2);
(*********************)
SM\[Beta][1,Subscript[g, 2]]:=\[Kappa] Subscript[g, 2]^4 (-(19/6));
SM\[Beta][2,Subscript[g, 2]]:=SM\[Beta][1,Subscript[g, 2]]+\[Kappa]^2 Subscript[g, 2]^4 (12 Subscript[g, 3]^2+35/6 Subscript[g, 2]^2+9/10 Subscript[g, 1]^2-3/2 Subscript[g, t]^2-3/2 Subscript[g, b]^2-1/2 Subscript[g, \[Tau]]^2);
SM\[Beta][3,Subscript[g, 2]]:=SM\[Beta][2,Subscript[g, 2]]+\[Kappa]^3 Subscript[g, 2]^4 (Subscript[g, t]^2 (147/16 Subscript[g, t]^2-7 Subscript[g, 3]^2-729/32 Subscript[g, 2]^2-593/160 Subscript[g, 1]^2)+\[Lambda] (-3 \[Lambda]+3/2 Subscript[g, 2]^2+3/10 Subscript[g, 1]^2)+81 Subscript[g, 3]^4+(324953 Subscript[g, 2]^4)/1728-(5597 Subscript[g, 1]^4)/1600+39 Subscript[g, 3]^2 Subscript[g, 2]^2-1/5 Subscript[g, 3]^2 Subscript[g, 1]^2+873/160 Subscript[g, 2]^2 Subscript[g, 1]^2);
(**********************)
SM\[Beta][1,Subscript[g, 3]]:=\[Kappa] Subscript[g, 3]^4 (-7);
SM\[Beta][2,Subscript[g, 3]]:=SM\[Beta][1,Subscript[g, 3]]+\[Kappa]^2 Subscript[g, 3]^4 (-26 Subscript[g, 3]^2+9/2 Subscript[g, 2]^2+11/10 Subscript[g, 1]^2-2 Subscript[g, t]^2-2 Subscript[g, b]^2);
SM\[Beta][3,Subscript[g, 3]]:=SM\[Beta][2,Subscript[g, 3]]+\[Kappa]^3 Subscript[g, 3]^4 (Subscript[g, t]^2 (15 Subscript[g, t]^2-40 Subscript[g, 3]^2-93/8 Subscript[g, 2]^2-101/40 Subscript[g, 1]^2)+65/2 Subscript[g, 3]^4+109/8 Subscript[g, 2]^4-523/120 Subscript[g, 1]^4+21 Subscript[g, 3]^2 Subscript[g, 2]^2+77/15 Subscript[g, 3]^2 Subscript[g, 1]^2-3/40 Subscript[g, 2]^2 Subscript[g, 1]^2)+0 1/(4 \[Pi])^8 Subscript[g, 3]^10 (-(61807/25));
(**We multiplied by 2\[Lambda] to have all the RGEs in the form ((dg^2)/(d Log[\[Mu]^2]))=Subscript[\[Beta], g]**)
SM\[Beta][1,\[Lambda]]:=(\[Kappa] 2\[Lambda])(\[Lambda] (12 \[Lambda]+6 Subscript[g, t]^2+6 Subscript[g, b]^2+2 Subscript[g, \[Tau]]^2-9/2 Subscript[g, 2]^2-9/10 Subscript[g, 1]^2)-3 Subscript[g, t]^4-3 Subscript[g, b]^4-Subscript[g, \[Tau]]^4+9/16 Subscript[g, 2]^4+27/400 Subscript[g, 1]^4+9/40 Subscript[g, 2]^2 Subscript[g, 1]^2);
SM\[Beta][2,\[Lambda]]:=SM\[Beta][1,\[Lambda]]+(\[Kappa]^2 2\[Lambda])(\[Lambda]^2 (-156 \[Lambda]-72 Subscript[g, t]^2-72 Subscript[g, b]^2-24 Subscript[g, \[Tau]]^2+54 Subscript[g, 2]^2+54/5 Subscript[g, 1]^2)+\[Lambda] Subscript[g, t]^2 (-(1/2) (3 Subscript[g, t]^2)-21 Subscript[g, b]^2+40 Subscript[g, 3]^2+45/4 Subscript[g, 2]^2+17/4 Subscript[g, 1]^2)+\[Lambda] Subscript[g, b]^2 (-(1/2) (3 Subscript[g, b]^2)+40 Subscript[g, 3]^2+45/4 Subscript[g, 2]^2+5/4 Subscript[g, 1]^2)+\[Lambda] Subscript[g, \[Tau]]^2 (-(1/2) Subscript[g, \[Tau]]^2+15/4 Subscript[g, 2]^2+15/4 Subscript[g, 1]^2)+\[Lambda] (-(1/16) (73 Subscript[g, 2]^4)+1887/400 Subscript[g, 1]^4+117/40 Subscript[g, 2]^2 Subscript[g, 1]^2)+Subscript[g, t]^4 (15 Subscript[g, t]^2-3 Subscript[g, b]^2-16 Subscript[g, 3]^2-4/5 Subscript[g, 1]^2)+Subscript[g, t]^2 (-(1/8) (9 Subscript[g, 2]^4)-171/200 Subscript[g, 1]^4+63/20 Subscript[g, 2]^2 Subscript[g, 1]^2)+Subscript[g, b]^4 (-3 Subscript[g, t]^2+15 Subscript[g, b]^2-16 Subscript[g, 3]^2+2/5 Subscript[g, 1]^2)+Subscript[g, b]^2 (-(1/8) (9 Subscript[g, 2]^4)+9/40 Subscript[g, 1]^4+27/20 Subscript[g, 2]^2 Subscript[g, 1]^2)+Subscript[g, \[Tau]]^4 (5 Subscript[g, \[Tau]]^2-6/5 Subscript[g, 1]^2)+Subscript[g, \[Tau]]^2 (-(1/8) (3 Subscript[g, 2]^4)-9/8 Subscript[g, 1]^4+33/20 Subscript[g, 2]^2 Subscript[g, 1]^2)+305/32 Subscript[g, 2]^6-(3411 Subscript[g, 1]^6)/4000-289/160 Subscript[g, 2]^4 Subscript[g, 1]^2-1677/800 Subscript[g, 2]^2 Subscript[g, 1]^4);
SM\[Beta][3,\[Lambda]]:=SM\[Beta][2,\[Lambda]]+(\[Kappa]^3 2\[Lambda])(-((377 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(8\)]\))/250)-(1543 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(6\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/1000+13/2 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\)-(37889 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(6\)]\))/1000-(114091 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(8\)]\))/1000+\[Lambda]^2 (-((46383 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/250)-7916/25 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)-(19757 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/25)+((663 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(6\)]\))/1000+221/200 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+(1507 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/1000+(942 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(6\)]\))/125) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)+\[Lambda] 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\) ((39819 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/500+(865483 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/1000-(7143 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/125)+\[Lambda] 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) ((3521 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/125+(61753 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/1000-(8381 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/1000)+\!\(
\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\ \((
\*FractionBox[\(11117\ 
\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\), \(1000\)] + 
\*FractionBox[\(10627\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\), \(1000\)])\)\ 
\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+\!\(
\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\ \((
\*FractionBox[\(13041\ 
\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\), \(1000\)] + 
\*FractionBox[\(125\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\), \(2\)])\)\ 
\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+((127 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/125+5693/500 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+(2058 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/125) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+\[Lambda] (-((748599 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/10000)+1123/200 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)-(39958 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/125+8727/500 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)+(151443 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/10000+(44621 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(4\)]\))/125) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+((3987 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/250-17589/250 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+(3971 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/250+1757/100 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)+(13349 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/1000-(50201 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(4\)]\))/1000) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\)+\!\(
\*SubsuperscriptBox[\(g\), \(t\), \(6\)]\ \((
\*FractionBox[\(3393\ 
\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\), \(100\)] + 
\*FractionBox[\(37069\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\), \(500\)] + 
\*FractionBox[\(125247\ 
\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\), \(500\)] - 
\*FractionBox[\(243149\ 
\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\), \(1000\)])\)\)+\[Lambda] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\) (-((4203 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/200)-(547 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/100-(331433 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/500-(111691 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))/500)+\[Lambda]^3 ((120227 \[Lambda])/20-(7749 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/100-(96863 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/250+873 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))+\[Lambda]^2 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (-((63869 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/1000)-(359539 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/1000+(16077 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/100+(88413 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))/50));
(***************)
SM\[Beta][1,Subscript[g, t]]:=\[Kappa] Subscript[g, t]^2 (9/2 Subscript[g, t]^2+3/2 Subscript[g, b]^2+Subscript[g, \[Tau]]^2-8 Subscript[g, 3]^2-9/4 Subscript[g, 2]^2-17/20 Subscript[g, 1]^2);
SM\[Beta][2,Subscript[g, t]]:=SM\[Beta][1,Subscript[g, t]]+\[Kappa]^2 Subscript[g, t]^2 (Subscript[g, t]^2 (-12 Subscript[g, t]^2-11/4 Subscript[g, b]^2-9/4 Subscript[g, \[Tau]]^2-12 \[Lambda]+36 Subscript[g, 3]^2+225/16 Subscript[g, 2]^2+393/80 Subscript[g, 1]^2)+Subscript[g, b]^2 (-(1/4) Subscript[g, b]^2+5/4 Subscript[g, \[Tau]]^2+4 Subscript[g, 3]^2+99/16 Subscript[g, 2]^2+7/80 Subscript[g, 1]^2)+Subscript[g, \[Tau]]^2 (-(1/4) (9 Subscript[g, \[Tau]]^2)+15/8 Subscript[g, 2]^2+15/8 Subscript[g, 1]^2)+6 \[Lambda]^2-108 Subscript[g, 3]^4-23/4 Subscript[g, 2]^4+1187/600 Subscript[g, 1]^4+9 Subscript[g, 3]^2 Subscript[g, 2]^2+19/15 Subscript[g, 3]^2 Subscript[g, 1]^2-9/20 Subscript[g, 2]^2 Subscript[g, 1]^2);
SM\[Beta][3,Subscript[g, t]]:=SM\[Beta][2,Subscript[g, t]]+\[Kappa]^3 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) ((16099 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(6\)]\))/1000-2221/500 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)-(4743 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/1000+(169829 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(6\)]\))/1000+\[Lambda]^2 (-36 \[Lambda]+9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+45 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))+\[Lambda] (-((1089 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/400)+117/40 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)-(171 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/16)-(22319 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\))/1000-321/20 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)-2634/125 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)-1887/125 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(4\)]\)+36827/500 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(4\)]\)-(12387 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(6\)]\))/20+\[Lambda] ((15 \[Lambda])/4-(127 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/10-(135 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/2+16 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+(-((12211 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/500)+(34829 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))/1000+(1699 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))/100+9037/500 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)+4837/100 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)+(90941 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(4\)]\))/250) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\)+\!\(
\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\ \((198\ \[Lambda] - 
\*FractionBox[\(2437\ 
\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\), \(80\)] - 
\*FractionBox[\(1593\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\), \(16\)] - 157\ 
\*SubsuperscriptBox[\(g\), \(3\), \(2\)] + 
\*FractionBox[\(146507\ 
\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\), \(2500\)])\)\));
(*************************)
SM\[Beta][1,Subscript[g, b]]:=\[Kappa] Subscript[g, b]^2 (3/2 Subscript[g, t]^2+9/2 Subscript[g, b]^2+Subscript[g, \[Tau]]^2-8 Subscript[g, 3]^2-9/4 Subscript[g, 2]^2-1/4 Subscript[g, 1]^2);
SM\[Beta][2,Subscript[g, b]]:=SM\[Beta][1,Subscript[g, b]]+\[Kappa]^2 Subscript[g, b]^2 (Subscript[g, t]^2 (-(1/4) Subscript[g, t]^2-11/4 Subscript[g, b]^2+5/4 Subscript[g, \[Tau]]^2+4 Subscript[g, 3]^2+99/16 Subscript[g, 2]^2+91/80 Subscript[g, 1]^2)+Subscript[g, b]^2 (-12 Subscript[g, b]^2-9/4 Subscript[g, \[Tau]]^2-12 \[Lambda]+36 Subscript[g, 3]^2+225/16 Subscript[g, 2]^2+237/80 Subscript[g, 1]^2)+Subscript[g, \[Tau]]^2 (-(1/4) (9 Subscript[g, \[Tau]]^2)+15/8 Subscript[g, 2]^2+15/8 Subscript[g, 1]^2)+6 \[Lambda]^2-108 Subscript[g, 3]^4-23/4 Subscript[g, 2]^4-127/600 Subscript[g, 1]^4+9 Subscript[g, 3]^2 Subscript[g, 2]^2+31/15 Subscript[g, 3]^2 Subscript[g, 1]^2-27/20 Subscript[g, 2]^2 Subscript[g, 1]^2);
SM\[Beta][3,Subscript[g, b]]:=SM\[Beta][2,Subscript[g, b]];(*defined for convenience*)
(******************)
SM\[Beta][1,Subscript[g, \[Tau]]]:=\[Kappa] Subscript[g, \[Tau]]^2 (3 Subscript[g, t]^2+3 Subscript[g, b]^2+5/2 Subscript[g, \[Tau]]^2-9/4 Subscript[g, 2]^2-9/4 Subscript[g, 1]^2);
SM\[Beta][2,Subscript[g, \[Tau]]]:=SM\[Beta][1,Subscript[g, \[Tau]]]+\[Kappa]^2 Subscript[g, \[Tau]]^2 (6 \[Lambda]^2-23/4 Subscript[g, 2]^4+1371/200 Subscript[g, 1]^4+27/20 Subscript[g, 2]^2 Subscript[g, 1]^2+Subscript[g, t]^2 (-(1/4) (27 Subscript[g, t]^2)+3/2 Subscript[g, b]^2-27/4 Subscript[g, \[Tau]]^2+20 Subscript[g, 3]^2+45/8 Subscript[g, 2]^2+17/8 Subscript[g, 1]^2)+Subscript[g, b]^2 (-(1/4) (27 Subscript[g, b]^2)-27/4 Subscript[g, \[Tau]]^2+20 Subscript[g, 3]^2+45/8 Subscript[g, 2]^2+5/8 Subscript[g, 1]^2)+Subscript[g, \[Tau]]^2 (-3 Subscript[g, \[Tau]]^2-12 \[Lambda]+165/16 Subscript[g, 2]^2+537/80 Subscript[g, 1]^2));
SM\[Beta][3,Subscript[g, \[Tau]]]:=SM\[Beta][2,Subscript[g, \[Tau]]] (*defined for convenience*)
]


(* ::Section::Closed:: *)
(*Running*)


SMrun[variables_,init_,tmin_,tmax_,opts:OptionsPattern[]]:=Block[{equations,vars,reps},
reps={Subscript[g, 1]->g1,Subscript[g, 2]->g2,Subscript[g, 3]->g3,Subscript[g, t]->gt,Subscript[g, \[Tau]]->g\[Tau],Subscript[g, b]->gb};
equations=Join[#[t]#'[t]==(SM\[Beta][3,#] /.(#->#[t]&/@variables))&/@variables,init]/.reps;
vars=variables/.reps;
First[NDSolve[equations,vars,{t,tmin,tmax},FilterRules[{opts},Options[NDSolve]]]] ]
optsSMrun={AccuracyGoal->5,PrecisionGoal->5,MaxSteps->350,If[$VersionNumber>=10,Method->{"Shooting","StartingInitialConditions"->{\[Lambda][35]==0.15}},Method->Automatic]};


(* ::Title::Closed:: *)
(*Split RGEs*)


(* ::Text:: *)
(*This sub-package solves the renormalization group equations of Split Supersymmetry. *)


(* ::Section::Closed:: *)
(*Preambula*)


(*Split\[Beta]::usage="Split\[Beta][loops,coupling] gives the Split \[Beta]-function of a coupling up to a given order specified by loops";
Splitrun::usage="run[variables,initialconds,tmin,tmax,opts] solves the coupled RGEs of the variables with the initial coditions given by initialconds between tmin and tmax. 
 It accepts the options of NDSolve. For time saving we recommend the optsrun";
optsSplitrun::usage="Default options for the function run. It selects the numerical method used by NDSolve and the precision goal";
{(*\[Lambda],Subscript[g, 3],Subscript[g, 2],Subscript[g, 1],Subscript[g, t],Subscript[g, \[Tau]],Subscript[g, b],g3,g2,g1,gt,g\[Tau],gb,*)Subscript[Overscript[g, ~], 1 u],Subscript[Overscript[g, ~], 2 u],Subscript[Overscript[g, ~], 1 d],Subscript[Overscript[g, ~], 2 d],gtildeu,gtilde2u,gtilded,gtilde2d};
(*The names of the couplings are not encapsulated.*)*)


(* ::Section::Closed:: *)
(*Beta Functions*)


Split\[Beta][1,coupling_]:=1/(4\[Pi])^2 Subscript[\[Beta], 1][coupling]
Split\[Beta][2,coupling_]:=1/(4\[Pi])^2 Subscript[\[Beta], 1][coupling]+1/(4\[Pi])^4 Subscript[\[Beta], 2][coupling]


(* ::Subsubsection::Closed:: *)
(*eqs. (26) : \[Beta] tilde*)


Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), t]:=1/2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2); Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]]:=2 \[Lambda](Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2);


(* ::Subsubsection::Closed:: *)
(*eq.  (35)-(36) : Subscript[\[Beta], 1] *)


Subscript[\[Beta], 1][Subscript[g, 1]]:=9/2 Subscript[g, 1]^3;Subscript[\[Beta], 1][Subscript[g, 2]]:=-(7/6) Subscript[g, 2]^3 ;Subscript[\[Beta], 1][Subscript[g, 3]]:=-5 Subscript[g, 3]^3;
Subscript[\[Beta], 1][Subscript[g, t]]:=Subscript[g, t] (Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), t]+3/2 Subscript[g, b]^2+Subscript[g, \[Tau]]^2+9/2 Subscript[g, t]^2-17/20 Subscript[g, 1]^2-9/4 Subscript[g, 2]^2-8 Subscript[g, 3]^2);Subscript[\[Beta], 1][Subscript[g, b]]:=Subscript[g, b] (Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), t]+3/2 Subscript[g, t]^2+Subscript[g, \[Tau]]^2+9/2 Subscript[g, b]^2-1/4 Subscript[g, 1]^2-9/4 Subscript[g, 2]^2-8 Subscript[g, 3]^2);Subscript[\[Beta], 1][Subscript[g, \[Tau]]]:=Subscript[g, \[Tau]] (Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), t]+3 Subscript[g, b]^2+3 Subscript[g, t]^2+5/2 Subscript[g, \[Tau]]^2-9/4 Subscript[g, 1]^2-9/4 Subscript[g, 2]^2);Subscript[\[Beta], 1][Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]]:=Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u] (3/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+1/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+11/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[g, b]^2+3 Subscript[g, t]^2+Subscript[g, \[Tau]]^2-9/20 Subscript[g, 1]^2-33/4 Subscript[g, 2]^2);Subscript[\[Beta], 1][Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]]:=Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] (3/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+1/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+11/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+3 Subscript[g, b]^2+3 Subscript[g, t]^2+Subscript[g, \[Tau]]^2-9/20 Subscript[g, 1]^2-33/4 Subscript[g, 2]^2);Subscript[\[Beta], 1][Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]]:=3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] (2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+5/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+9/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+3 Subscript[g, b]^2+3 Subscript[g, t]^2+Subscript[g, \[Tau]]^2-9/20 Subscript[g, 1]^2-9/4 Subscript[g, 2]^2);Subscript[\[Beta], 1][Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]]:=3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] (2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+5/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+3/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+9/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[g, b]^2+3 Subscript[g, t]^2+Subscript[g, \[Tau]]^2-9/20 Subscript[g, 1]^2-9/4 Subscript[g, 2]^2);Subscript[\[Beta], 1][\[Lambda]]:=4 \[Lambda] (3 Subscript[g, t]^2+3 Subscript[g, b]^2+Subscript[g, \[Tau]]^2)-9 \[Lambda] (1/5 Subscript[g, 1]^2+Subscript[g, 2]^2)-4 (3 Subscript[g, t]^4+3 Subscript[g, b]^4+Subscript[g, \[Tau]]^4)+27/100 Subscript[g, 1]^4+9/10 Subscript[g, 2]^2 Subscript[g, 1]^2+9/4 Subscript[g, 2]^4+12 \[Lambda]^2+Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]];


(* ::Subsubsection::Closed:: *)
(*eq. (37) - (39) : Subscript[\[Beta], 2] of the gauge couplings*)


Subscript[\[Beta], 2][Subscript[g, 1]]:=Subscript[g, 1]^3 (1/20 (-3) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2)-9/20 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)-1/2 Subscript[g, b]^2-17/10 Subscript[g, t]^2-3/2 Subscript[g, \[Tau]]^2+104/25 Subscript[g, 1]^2+18/5 Subscript[g, 2]^2+44/5 Subscript[g, 3]^2);
Subscript[\[Beta], 2][Subscript[g, 2]]:=Subscript[g, 2]^3 (-(1/4) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2)-11/4 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)-1/2 (3 Subscript[g, b]^2+3 Subscript[g, t]^2+Subscript[g, \[Tau]]^2)+6/5 Subscript[g, 1]^2+106/3 Subscript[g, 2]^2+12 Subscript[g, 3]^2);
Subscript[\[Beta], 2][Subscript[g, 3]]:=Subscript[g, 3]^3 (-2 (Subscript[g, b]^2+Subscript[g, t]^2)+11/10 Subscript[g, 1]^2+9/2 Subscript[g, 2]^2+22 Subscript[g, 3]^2)


(* ::Subsubsection::Closed:: *)
(*eqs. (40) - (47): Subscript[\[Beta], 2] of the rest of the couplings*)


Subscript[\[Beta], 2][Subscript[g, t]]:=-12 Subscript[g, t]^5+Subscript[g, t] (Subscript[g, b]^2 (5/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+5/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+15/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+15/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+5/4 Subscript[g, \[Tau]]^2+7/80 Subscript[g, 1]^2+99/16 Subscript[g, 2]^2+4 Subscript[g, 3]^2)+Subscript[g, 1]^2 (3/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+3/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-9/20 Subscript[g, 2]^2+19/15 Subscript[g, 3]^2)-3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[g, 2]^2 (15/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+15/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+165/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+165/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+9 Subscript[g, 3]^2)-5/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-3/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-45/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-45/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-1/4 Subscript[g, b]^4-9/4 Subscript[g, \[Tau]]^4+(15/8 Subscript[g, 1]^2+15/8 Subscript[g, 2]^2) Subscript[g, \[Tau]]^2+1303/600 Subscript[g, 1]^4-17/4 Subscript[g, 2]^4-284/3 Subscript[g, 3]^4+(3 \[Lambda]^2)/2)+Subscript[g, t]^3 (-(1/8) (9 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2)-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2-27/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-27/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-11/4 Subscript[g, b]^2-9/4 Subscript[g, \[Tau]]^2+393/80 Subscript[g, 1]^2+225/16 Subscript[g, 2]^2+36 Subscript[g, 3]^2-6 \[Lambda]) ;
Subscript[\[Beta], 2][Subscript[g, b]]:=-12 Subscript[g, b]^5+Subscript[g, b] (Subscript[g, t]^2 (5/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+5/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+15/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+15/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+5/4 Subscript[g, \[Tau]]^2+91/80 Subscript[g, 1]^2+99/16 Subscript[g, 2]^2+4 Subscript[g, 3]^2)+Subscript[g, 1]^2 (3/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+3/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-27/20 Subscript[g, 2]^2+31/15 Subscript[g, 3]^2)-3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[g, 2]^2 (15/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+15/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+165/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+165/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+9 Subscript[g, 3]^2)-5/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-3/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-45/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-45/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-1/4 Subscript[g, t]^4-9/4 Subscript[g, \[Tau]]^4+(15/8 Subscript[g, 1]^2+15/8 Subscript[g, 2]^2) Subscript[g, \[Tau]]^2-131/600 Subscript[g, 1]^4-17/4 Subscript[g, 2]^4-284/3 Subscript[g, 3]^4+(3 \[Lambda]^2)/2)+Subscript[g, b]^3 (-(1/8) (9 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2)-9/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2-27/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-27/8 Subscript[
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Subscript[\[Beta], 2][Subscript[g, \[Tau]]]:=-3 Subscript[g, \[Tau]]^5+Subscript[g, \[Tau]] (Subscript[g, 1]^2 (3/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+3/16 Subscript[
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Subscript[\[Beta], 2][Subscript[
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Subscript[\[Beta], 2][Subscript[
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Subscript[\[Beta], 2][Subscript[
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Subscript[\[Beta], 2][Subscript[
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\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-75/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-9/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-21/8 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-99/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-45/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-27/4 Subscript[g, b]^4-27/4 Subscript[g, t]^4-9/4 Subscript[g, \[Tau]]^4+117/200 Subscript[g, 1]^4-17/4 Subscript[g, 2]^4+(3 \[Lambda]^2)/2)+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^3 (-(1/4) (15 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2)-9/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-27/16 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-27/8 Subscript[g, b]^2-27/8 Subscript[g, t]^2-9/8 Subscript[g, \[Tau]]^2+309/160 Subscript[g, 1]^2+165/32 Subscript[g, 2]^2-3 \[Lambda])-6 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-3/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^5-9 Subscript[g, b]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-3 \[Lambda] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-9 Subscript[g, t]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-3 Subscript[g, \[Tau]]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-33/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^3-9/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-9/4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+9/20 Subscript[g, 1]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+51/4 Subscript[g, 2]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u] ;
Subscript[\[Beta], 2][\[Lambda]]:=-78 \[Lambda]^3-(3699 Subscript[g, 1]^6)/1000+(9/10 Subscript[g, b]^2-171/50 Subscript[g, t]^2-9/2 Subscript[g, \[Tau]]^2-9/100 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)) Subscript[g, 1]^4+(8/5 Subscript[g, b]^4-16/5 Subscript[g, t]^4-24/5 Subscript[g, \[Tau]]^4) Subscript[g, 1]^2+209/8 Subscript[g, 2]^6+20 (3 Subscript[g, b]^6+3 Subscript[g, t]^6+Subscript[g, \[Tau]]^6)-64 Subscript[g, 3]^2 Subscript[g, b]^4-(64 Subscript[g, 3]^2+12 Subscript[g, b]^2) Subscript[g, t]^4-12 Subscript[g, b]^4 Subscript[g, t]^2+\[Lambda]^2 (54/5 Subscript[g, 1]^2+54 Subscript[g, 2]^2-72 Subscript[g, b]^2-72 Subscript[g, t]^2-24 Subscript[g, \[Tau]]^2-12 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2))+Subscript[g, 2]^4 (-(1/8) (77 Subscript[g, 1]^2)-9/2 Subscript[g, b]^2-9/2 Subscript[g, t]^2-3/2 Subscript[g, \[Tau]]^2-3/4 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+51 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+51 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2))+Subscript[g, 2]^2 (-(1/200) (1773 Subscript[g, 1]^4)+(27/5 Subscript[g, b]^2+63/5 Subscript[g, t]^2+33/5 Subscript[g, \[Tau]]^2-3/10 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2-21 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-21 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)) Subscript[g, 1]^2-4 (5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]+5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2))+\[Lambda] (2007/200 Subscript[g, 1]^4+(5/2 Subscript[g, b]^2+17/2 Subscript[g, t]^2+15/2 Subscript[g, \[Tau]]^2+3/4 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)) Subscript[g, 1]^2+47/8 Subscript[g, 2]^4-3 Subscript[g, b]^4-3 Subscript[g, t]^4-Subscript[g, \[Tau]]^4+80 Subscript[g, 3]^2 Subscript[g, b]^2+(80 Subscript[g, 3]^2-42 Subscript[g, b]^2) Subscript[g, t]^2+1/4 (-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2-6 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2) Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+80 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2-44 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)+Subscript[g, 2]^2 (117/20 Subscript[g, 1]^2+45/2 Subscript[g, b]^2+45/2 Subscript[g, t]^2+15/2 Subscript[g, \[Tau]]^2+15/4 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+11 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+11 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)))+1/2 (47 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^6+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^6)+5 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^6+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^6)+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u](42 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+42 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+38 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+38 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2)+19 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)+21 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u](Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2)+17 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2)+11 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4)+7 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2));


(* ::Input:: *)
(*(************************************************************************)*)


(* ::Section:: *)
(*Running*)


Splitrun[variables_,init_,tmin_,tmax_,opts:OptionsPattern[]]:=Block[{equations,vars,reps},
reps={Subscript[g, 1]->g1,Subscript[g, 2]->g2,Subscript[g, 3]->g3,Subscript[g, t]->gt,Subscript[g, \[Tau]]->g\[Tau],Subscript[g, b]->gb,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]->gtildeu,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]->gtilde2u,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]->gtilded,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]->gtilde2d};
equations=Join[#'[t]==(Split\[Beta][2,#] /.(#->#[t]&/@variables))&/@variables,init]/.reps;
vars=variables/.reps;
First[NDSolve[equations,vars,{t,tmin,tmax},FilterRules[{opts},Options[NDSolve]]]] 
]
optsSplitrun={AccuracyGoal->5,PrecisionGoal->5,MaxSteps->200};


(* ::Title:: *)
(*SUSY Thresholds*)


(* ::Text:: *)
(*This sub-package contains the threshold corrections to the quartic coupling of the Higgs in High Scale Supersymmetry and Split Supersymmetry. *)


(* ::Section::Closed:: *)
(*Preambula*)


(*\[Lambda]HSS::usage="\[Lambda]HSS[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the thresholds to the quartic coupling at scale of the scalar masses in High Scale Supersymmetry.";
hiOrd::usage="controls the inclusion of higher-order corrections";
scheme::usage="chooses the renormalization scheme";
suppressedCorrections::usage="v^2/Overscript[m, ~]^2-suppressed corrections";
\[Lambda]Splitscalars::usage="\[Lambda]Splitscalars[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the thresholds to the quartic coupling at the mass of the scalars in Split Supersymmetry.";
\[Lambda]SMsplit::usage="\[Lambda]SMsplit[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the quartic coupling of the Standard Model at the scale of the fermions obtained after integrating out all the supersymmetric particles.";
gtSplitsplit::usage="gtSplitsplit[\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3]] computes the top Yukawa coupling just above the scale of the fermion masses in Split Supersymmetry.";
g1umtilde::usage="g1umtilde[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the Higgs-higgsino-gaugino coupling at the mass of the scalar masses including the one-loop thresholds corrections.";
g2umtilde::usage="g2umtilde[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the Higgs-higgsino-gaugino coupling at the mass of the scalar masses including the one-loop thresholds corrections.";g1dmtilde::usage="g1dmtilde[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the Higgs-higgsino-gaugino coupling at the mass of the scalar masses including the one-loop thresholds corrections.";g2dmtilde::usage="g2dmtilde[Subscript[m, Subscript[Q, 1]],Subscript[m, Subscript[Q, 2]],Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 1]],Subscript[m, Subscript[U, 2]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 1]],Subscript[m, Subscript[D, 2]],Subscript[m, Subscript[D, 3]],Subscript[m, Subscript[E, 1]],Subscript[m, Subscript[E, 2]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[L, 1]],Subscript[m, Subscript[L, 2]],Subscript[m, Subscript[L, 3]],Subscript[m, A],\[Mu],Subscript[M, 1],Subscript[M, 2],Subscript[M, 3],\[Beta],Subscript[X, t]] computes the Higgs-higgsino-gaugino coupling at the mass of the scalar masses including the one-loop thresholds corrections.";
gbDR::usage="gbDR[Subscript[m, Subscript[Q, 3]],Subscript[m, Subscript[U, 3]],Subscript[m, Subscript[D, 3]],Subscript[M, 3],\[Mu],tan\[Beta],Subscript[X, t]] computes the Overscript[DR, _] bottom Yukawa.";
gtauDR::usage="gtauDR[Subscript[m, Subscript[L, 3]],Subscript[m, Subscript[E, 3]],Subscript[m, Subscript[N, 3]],Subscript[M, 2],Subscript[M, 1],\[Mu],tan\[Beta]] computes the Overscript[DR, _] bottom Yukawa.";
\[Lambda]HSS1lsuppressed::usage="It is used to estimate the v^2/Subscript[m, SUSY]^2-suppressed corrections."*)


(* ::Section:: *)
(*Thresholds MSSM*)


(* ::Subsection:: *)
(*One Loop*)


(* ::Subsubsection::Closed:: *)
(*Expressions one-loop*)


\[Lambda]HSS1laux:=\[Lambda]tree+\[CapitalDelta]\[Lambda]1lreg+\[CapitalDelta]\[Lambda]1l\[Phi]+\[CapitalDelta]\[Lambda]1l\[Chi]1HSS+\[CapitalDelta]\[Lambda]1l\[Chi]2
\[Lambda]HSS1lsuppressedaux:=factorscalars \[CapitalDelta]\[Lambda]1l\[Phi]+factorfermions (\[CapitalDelta]\[Lambda]1l\[Chi]1HSS+\[CapitalDelta]\[Lambda]1l\[Chi]2)
\[Lambda]Splitscalarsaux:=\[Lambda]tree+\[CapitalDelta]\[Lambda]1lreg+\[CapitalDelta]\[Lambda]1l\[Phi]
\[Lambda]SMsplitaux:=\[Lambda]+\[CapitalDelta]\[Lambda]1l\[Chi]1Split
gtSplitsplitaux:=Subscript[g, t](1+\[CapitalDelta]gt\[Chi])


\[Lambda]tree:=1/4 (Subscript[g, 2]^2+3/5 Subscript[g, 1]^2)Cos[2\[Beta]]^2
\[CapitalDelta]\[Lambda]1lreg:=1/(4\[Pi])^2 (-(9/100)  
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)-3/10 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)-(3/4-1/6 Cos[2 \[Beta]]^2) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\));(*eq. 9*)
\[CapitalDelta]\[Lambda]1l\[Phi]:=1/((4 \[Pi])^2)  (3 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\(g\), \(t\), \(2\)] + \(
\*FractionBox[\(1\), \(2\)]\ \((
\*SubsuperscriptBox[\(g\), \(2\), \(2\)] - 
\*FractionBox[
SubsuperscriptBox[\(g\), \(1\), \(2\)], \(5\)])\)\ Cos[2\ \[Beta]]\)\)) Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+3 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\(g\), \(t\), \(2\)] + \(
\*FractionBox[\(2\), \(5\)]\ 
\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\ Cos[2\ \[Beta]]\)\)) Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+1/300 (Cos[2 \[Beta]]^2) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\((3 \((
\*SubsuperscriptBox[\(g\), \(1\), \(4\)] + 25\ 
\*SubsuperscriptBox[\(g\), \(2\), \(4\)])\)\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 24\ 
\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 6\ 
\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(D\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + \((9\ 
\*SubsuperscriptBox[\(g\), \(1\), \(4\)] + 25\ 
\*SubsuperscriptBox[\(g\), \(2\), \(4\)])\)\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(L\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 18\ 
\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(E\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]])\)\)+1/4800 (261 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)+630 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+1325 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\)-4 Cos[4 \[Beta]] (9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)+90 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+175 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))-9 Cos[8 \[Beta]] (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))^2) Log[Subscript[m, A]^2/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]-3/16 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))^2 Sin[4 \[Beta]]^2+6 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\) Subscript[
\!\(\*OverscriptBox[\(X\), \(~\)]\), t] (Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][Subscript[x, QU]]-1/12 Subscript[
\!\(\*OverscriptBox[\(X\), \(~\)]\), t] Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][Subscript[x, QU]])+3/4 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(X\), \(~\)]\), t] Cos[2 \[Beta] ](3/5 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 3][Subscript[x, QU]]+\!\(
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\ \(
\(\*SubscriptBox[
OverscriptBox[\(F\), \(~\)], \(4\)]\)[
\*SubscriptBox[\(x\), \(QU\)]]\)\))-1/4 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(X\), \(~\)]\), t] Cos[2 \[Beta]]^2 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 5][Subscript[x, QU]]) (*eq. 10*)
Subscript[
\!\(\*OverscriptBox[\(X\), \(~\)]\), t]:=Subscript[X, t]^2/(Subscript[m, Subscript[Q, 3]] Subscript[m, Subscript[U, 3]]);Subscript[x, QU]:=Subscript[m, Subscript[Q, 3]]/Subscript[m, Subscript[U, 3]];


\[CapitalDelta]\[Lambda]1l\[Chi]1Split:=Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]] /((4 \[Pi])^2)  1/2 Log[\[Mu]^2/msplit^2]+1/(4 \[Pi])^2 (1/12 (-7) Subscript[f, 1][Subscript[r, 1]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(4\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(4\)]\))-9/4 Subscript[f, 2][Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(4\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(4\)]\))-3/2 Subscript[f, 3][Subscript[r, 1]] 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\) 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\)-7/2 Subscript[f, 4][Subscript[r, 2]] 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\) 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)-8/3 Subscript[f, 5][Subscript[r, 1],Subscript[r, 2]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-7/6 Subscript[f, 6][Subscript[r, 1],Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\)+\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\))-1/6 Subscript[f, 7][Subscript[r, 1],Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)+\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\))-4/3 Subscript[f, 8][Subscript[r, 1],Subscript[r, 2]] (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u])+2/3 f[Subscript[r, 1]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u](\[Lambda]-2 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\)))+2 f[Subscript[r, 2]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u](\[Lambda]-2 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)))+1/3 gg[Subscript[r, 1]] \[Lambda](\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\))+gg[Subscript[r, 2]] \[Lambda](\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)));(*eq. 11*)
Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]]:=2 \[Lambda](Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2); (*eq. 12*)
Subscript[r, 1]:=Subscript[M, 1]/\[Mu];Subscript[r, 2]:=Subscript[M, 2]/\[Mu];


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]1l\[Chi]1Split/.{msplit->*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\),Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]->(Subscript[g, 2] Sin[\[Beta]]),Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]->(Subscript[g, 2] Cos[\[Beta]]),Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]->(Sqrt[3/5] Subscript[g, 1] Sin[\[Beta]]),Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]->(Sqrt[3/5] Subscript[g, 1] Cos[\[Beta]]),\[Lambda]->\[Lambda]tree}//Simplify*)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]1l\[Chi]1HSS:=1/(6400 \[Pi]^2) (4 Cos[2 \[Beta]]^2 gg[Subscript[M, 1]/\[Mu]] *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) (3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+5 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))+3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) (-18 Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+6 Cos[4 \[Beta]] Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+f[Subscript[M, 1]/\[Mu]] (-31 Sin[2 \[Beta]]+Sin[6 \[Beta]])-7 (3+Cos[4 \[Beta]]) Subscript[f, 1][Subscript[M, 1]/\[Mu]]-9 Subscript[f, 3][Subscript[M, 1]/\[Mu]]+9 Cos[4 \[Beta]] Subscript[f, 3][Subscript[M, 1]/\[Mu]])+25 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\) (4 Cos[2 \[Beta]]^2 gg[Subscript[M, 2]/\[Mu]]-26 Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]-2 Cos[4 \[Beta]] Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+f[Subscript[M, 2]/\[Mu]] (-31 Sin[2 \[Beta]]+Sin[6 \[Beta]])-27 Subscript[f, 2][Subscript[M, 2]/\[Mu]]-9 Cos[4 \[Beta]] Subscript[f, 2][Subscript[M, 2]/\[Mu]]-7 Subscript[f, 4][Subscript[M, 2]/\[Mu]]+7 Cos[4 \[Beta]] Subscript[f, 4][Subscript[M, 2]/\[Mu]])+5 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) (6 (1+Cos[4 \[Beta]]) gg[Subscript[M, 2]/\[Mu]]-24 Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+24 Cos[4 \[Beta]] Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+3 f[Subscript[M, 2]/\[Mu]] Sin[2 \[Beta]]+3 f[Subscript[M, 2]/\[Mu]] Sin[6 \[Beta]]+f[Subscript[M, 1]/\[Mu]] (Sin[2 \[Beta]]+Sin[6 \[Beta]])-16 Subscript[f, 5][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]+16 Cos[4 \[Beta]] Subscript[f, 5][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]-42 Subscript[f, 6][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]-14 Cos[4 \[Beta]] Subscript[f, 6][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]-2 Subscript[f, 7][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]+2 Cos[4 \[Beta]] Subscript[f, 7][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]-64 Sin[2 \[Beta]] Subscript[f, 8][Subscript[M, 1]/\[Mu],Subscript[M, 2]/\[Mu]]));*)
(*\[CapitalDelta]\[Lambda]1l\[Chi]2:=1/(4\[Pi])^2 (-(1/6) Cos[2\[Beta]]^2 (2Subscript[g, 2]^4 Log[Subscript[M, 2]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+(9/25 Subscript[g, 1]^4+Subscript[g, 2]^4)Log[\[Mu]^2/*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)^2])); (*eq. 13*)*)
(**)


\[CapitalDelta]\[Lambda]1l\[Chi]1Split:=Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]] /((4 \[Pi])^2)  1/2 Log[\[Mu]^2/msplit^2]+1/(4 \[Pi])^2 (1/12 (-7) Subscript[f, 1][Subscript[r, 1]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(4\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(4\)]\))-9/4 Subscript[f, 2][Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(4\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(4\)]\))-3/2 Subscript[f, 3][Subscript[r, 1]] 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\) 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\)-7/2 Subscript[f, 4][Subscript[r, 2]] 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\) 
\!\(\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)-8/3 Subscript[f, 5][Subscript[r, 1],Subscript[r, 2]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-7/6 Subscript[f, 6][Subscript[r, 1],Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\)+\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\))-1/6 Subscript[f, 7][Subscript[r, 1],Subscript[r, 2]] (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)+\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\ 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\))-4/3 Subscript[f, 8][Subscript[r, 1],Subscript[r, 2]] (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u])+2/3 f[Subscript[r, 1]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u](\[Lambda]-2 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\)))+2 f[Subscript[r, 2]] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u](\[Lambda]-2 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)))+1/3 gg[Subscript[r, 1]] \[Lambda](\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)]\))+gg[Subscript[r, 2]] \[Lambda](\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)]\)));(*eq. 11*)
Subscript[
\!\(\*OverscriptBox[\(\[Beta]\), \(~\)]\), \[Lambda]]:=2 \[Lambda](Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2+3 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2)-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^4-Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^4-5 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^4-4 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]-2 (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]^2) (Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]^2+Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]^2); (*eq. 12*)
Subscript[r, 1]:=Subscript[M, 1]/\[Mu];Subscript[r, 2]:=Subscript[M, 2]/\[Mu];


g2umtildeaux:=Subscript[g, 2] Sin[\[Beta]](1+1/(4 \[Pi])^2 (-
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)(2/3+(11 Cos[\[Beta]]^2)/16)+1/80 (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)) (-2+7 Cos[\[Beta]]^2)+(9 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))/(4 Sin[\[Beta]]^2)+(20 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+3 (-9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+35 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))Cos[\[Beta]]^2)/120 Log[Subscript[m, A]^2/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+1/6 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\(Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(L\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]]\)\)+1/2 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\(Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]]\)\)-(3 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) )/(4 (Sin[\[Beta]]^2)) (3 Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]-Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]))) ;
g2dmtildeaux:=Subscript[g, 2]Cos[\[Beta]](1+1/(4 \[Pi])^2 (-
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)(2/3+(11 Sin[\[Beta]]^2)/16)+1/80 (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)) (-2+7 Sin[\[Beta]]^2)+1/2 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\(Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]]\)\)+1/120 (20 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+3 (-9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+35 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) Sin[\[Beta]]^2) Log[
\!\(\*SubsuperscriptBox[\(m\), \(A\), \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+1/6 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\(Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(L\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]]\)\)) );
g1umtildeaux:=Sqrt[3/5] Subscript[g, 1] Sin[\[Beta]](1+1/(4 \[Pi])^2 (1/16 (3 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) (-2+7 Cos[\[Beta]]^2)+1/80 (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)) (-44+7 Cos[\[Beta]]^2)+(9 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))/(4 Sin[\[Beta]]^2)+1/40 (4 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)-9 (\!\(
\*SubsuperscriptBox[\(g\), \(1\), \(2\)] + \(5\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)\)) Cos[\[Beta]]^2) Log[
\!\(\*SubsuperscriptBox[\(m\), \(A\), \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+1/10 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\((Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(L\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 2\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(E\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]])\)\)+1/30 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\((Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 8\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 2\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(D\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]])\)\)+\!\(
\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\(\ \)\)/(4 Sin[\[Beta]]^2) (7 Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]-13 Log[
\!\(\*SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(3\)], \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]))) ;
g1dmtildeaux:=Sqrt[3/5] Subscript[g, 1] Cos[\[Beta]](1+1/(4 \[Pi])^2 (1/16 (3 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) (-2+7 Sin[\[Beta]]^2)+1/80 (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)) (-44+7 Sin[\[Beta]]^2)+1/40 (4 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)-9 (\!\(
\*SubsuperscriptBox[\(g\), \(1\), \(2\)] + \(5\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)\)) Sin[\[Beta]]^2) Log[
\!\(\*SubsuperscriptBox[\(m\), \(A\), \(2\)]\)/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]+1/10 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\((Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(L\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 2\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(E\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]])\)\)+1/30 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\((Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(Q\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 8\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(U\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]] + 2\ Log[
\*FractionBox[
SubsuperscriptBox[\(m\), 
SubscriptBox[\(D\), \(i\)], \(2\)], 
SuperscriptBox[
OverscriptBox[\(m\), \(~\)], \(2\)]]])\)\))) ;
 \[CapitalDelta]gt\[Chi]:=1/(4 \[Pi])^2 (-(1/6) Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d] f[Subscript[M, 1]/\[Mu]]-1/12 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ u\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(1\ d\), \(2\)]\)) (gg[Subscript[M, 1]/\[Mu]]+3 Log[\[Mu]^2/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2])-1/2 Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u] Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d] f[Subscript[M, 2]/\[Mu]]-1/4 (\!\(
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ u\), \(2\)] + 
\*SubsuperscriptBox[
OverscriptBox[\(g\), \(~\)], \(2\ d\), \(2\)]\)) (gg[Subscript[M, 2]/\[Mu]]+3 Log[\[Mu]^2/
\!\(\*OverscriptBox[\(m\), \(~\)]\)^2]))/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->msplit};


(* ::Subsubsection::Closed:: *)
(*Loop Functions*)


(* ::Text:: *)
(*When evaluating the loop functions, the limit values need to be treated carefully to avoid indeterminate expressions.*)


(* ::Input::Closed:: *)
(*(*Commented*)*)


(* ::Input:: *)
(*(*With[{\[Delta]=10^-7},Subscript[Overscript[F, ~], 1][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},(x Log[x^2])/(x^2-1)];Subscript[Overscript[F, ~], 2][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},(6 x^2 (2-2 x^2+(1+x^2) Log[x^2]))/(x^2-1)^3];Subscript[Overscript[F, ~], 3][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},(2 x (5 (1-x^2)+(1+4 x^2) Log[x^2]))/(3 (x^2-1)^2)];Subscript[Overscript[F, ~], 4][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},(2 x (x^2-1-Log[x^2]))/(x^2-1)^2];Subscript[Overscript[F, ~], 5][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},(3 x (1-x^4+2 x^2 Log[x^2]))/(1-x^2)^3];Subscript[Overscript[F, ~], 6][x_]:=Piecewise[{{0,Abs[x-1]<\[Delta]}},(x^2-3)/(4 (1-x^2))+((x^2 (x^2-2)) Log[x^2])/(2 (1-x^2)^2)];Subscript[Overscript[F, ~], 7][x_]:=Piecewise[{{1,Abs[x-1]<\[Delta]}},-((3 (x^4-6 x^2+1))/(2 (x^2-1)^2))+((3 x^4 (x^2-3)) Log[x^2])/(x^2-1)^3];Subscript[Overscript[F, ~], 8][x1_,x2_]:=Piecewise[{{1,(Abs[x1-1]+Abs[x2-1])<\[Delta]}},-2+2 /(x1^2-x2^2)((x1^4 Log[x1^2])/(x1^2-1)-(x2^4 Log[x2^2])/(x2^2-1))];Subscript[Overscript[F, ~], 9][x1_,x2_]:=Piecewise[{{1,(Abs[x1-1]+Abs[x2-1])<\[Delta]}},(2 ((x1^2 Log[x1^2])/(x1^2-1)-(x2^2 Log[x2^2])/(x2^2-1)))/(x1^2-x2^2)];*)
(*f[r_]:=Subscript[Overscript[F, ~], 5][r];*)
(*gg[r_]:=Subscript[Overscript[F, ~], 7][r];(*define gg to avoid conflict*)*)
(*Subscript[f, 1][r_]:=Piecewise[{{1,Abs[r-1]<\[Delta]}},(6 (r^2+3) r^2)/(7 (r^2-1)^2)+(6 (r^2-5) r^4 Log[r^2])/(7 (r^2-1)^3)];*)
(*Subscript[f, 2][r_]:=Piecewise[{{1,Abs[r-1]<\[Delta]}},(2 (r^2+11) r^2)/(9 (r^2-1)^2)+(2 (5 r^2-17) r^4 Log[r^2])/(9 (r^2-1)^3)];Subscript[f, 3][r_]:=Piecewise[{{1,Abs[r-1]<\[Delta]}},(2 (r^4+9 r^2+2))/(3 (r^2-1)^2)+(2 (r^4-7 r^2-6) r^2 Log[r^2])/(3 (r^2-1)^3)];Subscript[f, 4][r_]:=Piecewise[{{1,Abs[r-1]<\[Delta]}},(2 (5 r^4+25 r^2+6))/(7 (r^2-1)^2)+(2 (r^4-19 r^2-18) r^2 Log[r^2])/(7 (r^2-1)^3)];Subscript[f, 5][r1_,r2_]:=Piecewise[{{1,(Abs[r1-1]+Abs[r2-1])<\[Delta]}},3/4 ((1+(r1+r2)^2-r1^2 r2^2)/((r1^2-1) (r2^2-1))+(r1^3 (r1^2+1) Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^3(r2^2+1) Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 6][r1_,r2_]:=Piecewise[{{1,(Abs[r1-1]+Abs[r2-1])<\[Delta]}},6/7 ((r1^2+r2^2+r1 r2-r1^2 r2^2)/((r1^2-1) (r2^2-1))+(r1^5 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^5 Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 7][r1_,r2_]:=Piecewise[{{1,(Abs[r1-1]+Abs[r2-1])<\[Delta]}},6 ((1+r1 r2)/((r1^2-1) (r2^2-1))+(r1^3 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^3 Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 8][r1_,r2_]:=Piecewise[{{1,(Abs[r1-1]+Abs[r2-1])<\[Delta]}},3/2 ((r1+r2)/((r1^2-1) (r2^2-1))+(r1^4 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^4 Log[r2^2])/((r1-r2) (r2^2-1)^2))];]*)*)


With[{\[Delta]=1.3564 10^-4,\[Delta]2=2.36547 10^-4},Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][Qx_]:=Block[{x=(1.+\[Delta])Qx},(x Log[x^2])/(x^2-1)];
Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][Qx_]:=Block[{x=(1.+\[Delta])Qx},(6 x^2 (2-2 x^2+(1+x^2) Log[x^2]))/(x^2-1)^3];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 3][Qx_]:=Block[{x=(1.+\[Delta])Qx},(2 x (5 (1-x^2)+(1+4 x^2) Log[x^2]))/(3 (x^2-1)^2)];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 4][Qx_]:=Block[{x=(1.+\[Delta])Qx},(2 x (x^2-1-Log[x^2]))/(x^2-1)^2];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 5][Qx_]:=Block[{x=(1.+\[Delta])Qx},(3 x (1-x^4+2 x^2 Log[x^2]))/(1-x^2)^3];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 6][Qx_]:=Block[{x=(1.+\[Delta])Qx},(x^2-3)/(4 (1-x^2))+((x^2 (x^2-2)) Log[x^2])/(2 (1-x^2)^2)];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 7][Qx_]:=Block[{x=(1.+\[Delta])Qx},-((3 (x^4-6 x^2+1))/(2 (x^2-1)^2))+((3 x^4 (x^2-3)) Log[x^2])/(x^2-1)^3];Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 8][Qx1_,Qx2_]:=Block[{x1=(1.+\[Delta])Qx1,x2=(1.+\[Delta]2)Qx2},-2+2 /(x1^2-x2^2) ((x1^4 Log[x1^2])/(x1^2-1)-(x2^4 Log[x2^2])/(x2^2-1))];
Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 9][Qx1_,Qx2_]:=Block[{x1=(1.+\[Delta])Qx1,x2=(1.+\[Delta]2)Qx2},(2 ((x1^2 Log[x1^2])/(x1^2-1)-(x2^2 Log[x2^2])/(x2^2-1)))/(x1^2-x2^2)];
f[r_]:=Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 5][r];
gg[r_]:=Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 7][r];(*define gg to avoid conflict*)
Subscript[f, 1][Qr_]:=Block[{r=(1.+\[Delta])Qr},(6 (r^2+3) r^2)/(7 (r^2-1)^2)+(6 (r^2-5) r^4 Log[r^2])/(7 (r^2-1)^3)];
Subscript[f, 2][Qr_]:=Block[{r=(1.+\[Delta])Qr},(2 (r^2+11) r^2)/(9 (r^2-1)^2)+(2 (5 r^2-17) r^4 Log[r^2])/(9 (r^2-1)^3)];Subscript[f, 3][Qr_]:=Block[{r=(1.+\[Delta])Qr},(2 (r^4+9 r^2+2))/(3 (r^2-1)^2)+(2 (r^4-7 r^2-6) r^2 Log[r^2])/(3 (r^2-1)^3)];Subscript[f, 4][Qr_]:=Block[{r=(1.+\[Delta])Qr},(2 (5 r^4+25 r^2+6))/(7 (r^2-1)^2)+(2 (r^4-19 r^2-18) r^2 Log[r^2])/(7 (r^2-1)^3)];Subscript[f, 5][Qr1_,Qr2_]:=Block[{r1=(1.+\[Delta])Qr1,r2=(1.+\[Delta]2)Qr2},3/4 ((1+(r1+r2)^2-r1^2 r2^2)/((r1^2-1) (r2^2-1))+(r1^3 (r1^2+1) Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^3 (r2^2+1) Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 6][Qr1_,Qr2_]:=Block[{r1=(1.+\[Delta])Qr1,r2=(1.+\[Delta]2)Qr2},6/7 ((r1^2+r2^2+r1 r2-r1^2 r2^2)/((r1^2-1) (r2^2-1))+(r1^5 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^5 Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 7][Qr1_,Qr2_]:=Block[{r1=(1.+\[Delta])Qr1,r2=(1.+\[Delta]2)Qr2},6 ((1+r1 r2)/((r1^2-1) (r2^2-1))+(r1^3 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^3 Log[r2^2])/((r1-r2) (r2^2-1)^2))];Subscript[f, 8][Qr1_,Qr2_]:=Block[{r1=(1.+\[Delta])Qr1,r2=(1.+\[Delta]2)Qr2},3/2 ((r1+r2)/((r1^2-1) (r2^2-1))+(r1^4 Log[r1^2])/((r1^2-1)^2 (r1-r2))-(r2^4 Log[r2^2])/((r1-r2) (r2^2-1)^2))]]


(* ::Subsubsection::Closed:: *)
(*One loop function HSS*)


(* ::Input:: *)
(*\[Lambda]HSS1laux/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt,*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}//Simplify*)


(* ::Input:: *)
(*\[Lambda]HSS1lsuppressedaux/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt,*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}//Simplify*)


\[Lambda]HSS1l[mtilde_,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=1./19200 (960 Cos[2 ArcTan[tan\[Beta]]]^2 (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))+(4 (-27 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)-90 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+25 (-8+Cos[4 ArcTan[tan\[Beta]]]) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\)))/\[Pi]^2-(200 Cos[2 ArcTan[tan\[Beta]]]^2 (2 Log[M2^2/mtilde^2] 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\)+Log[Q\[Mu]^2/mtilde^2] ((9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\))/25+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))))/\[Pi]^2+1/\[Pi]^2 3 (4 Cos[2 ArcTan[tan\[Beta]]]^2 gg[M1/Q\[Mu]] 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))+3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) (-18 Log[Q\[Mu]^2/mtilde^2]+6 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+f[M1/Q\[Mu]] (-31 Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-7 (3+Cos[4 ArcTan[tan\[Beta]]]) Subscript[f, 1][M1/Q\[Mu]]-9 Subscript[f, 3][M1/Q\[Mu]]+9 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 3][M1/Q\[Mu]])+25 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\) (4 Cos[2 ArcTan[tan\[Beta]]]^2 gg[M2/Q\[Mu]]-26 Log[Q\[Mu]^2/mtilde^2]-2 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+f[M2/Q\[Mu]] (-31 Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-27 Subscript[f, 2][M2/Q\[Mu]]-9 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 2][M2/Q\[Mu]]-7 Subscript[f, 4][M2/Q\[Mu]]+7 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 4][M2/Q\[Mu]])+5 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) (6 (1+Cos[4 ArcTan[tan\[Beta]]]) gg[M2/Q\[Mu]]-24 Log[Q\[Mu]^2/mtilde^2]+24 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+3 f[M2/Q\[Mu]] Sin[2 ArcTan[tan\[Beta]]]+3 f[M2/Q\[Mu]] Sin[6 ArcTan[tan\[Beta]]]+f[M1/Q\[Mu]] (Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-16 Subscript[f, 5][M1/Q\[Mu],M2/Q\[Mu]]+16 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 5][M1/Q\[Mu],M2/Q\[Mu]]-42 Subscript[f, 6][M1/Q\[Mu],M2/Q\[Mu]]-14 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 6][M1/Q\[Mu],M2/Q\[Mu]]-2 Subscript[f, 7][M1/Q\[Mu],M2/Q\[Mu]]+2 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 7][M1/Q\[Mu],M2/Q\[Mu]]-64 Sin[2 ArcTan[tan\[Beta]]] Subscript[f, 8][M1/Q\[Mu],M2/Q\[Mu]]))+1/\[Pi]^2 1200 (-(3/16) Sin[4 ArcTan[tan\[Beta]]]^2 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))^2-1/4800 Log[mA^2/mtilde^2] (9 (-29+4 Cos[4 ArcTan[tan\[Beta]]]+9 Cos[8 ArcTan[tan\[Beta]]]) 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)-360 (5+3 Cos[4 ArcTan[tan\[Beta]]]) Sin[2 ArcTan[tan\[Beta]]]^2 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+25 (-53+28 Cos[4 ArcTan[tan\[Beta]]]+9 Cos[8 ArcTan[tan\[Beta]]]) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))+1/300 Cos[2 ArcTan[tan\[Beta]]]^2 (3 (2 Log[mD1^2/mtilde^2]+2 Log[mD2^2/mtilde^2]+2 Log[mD3^2/mtilde^2]+6 Log[mE1^2/mtilde^2]+6 Log[mE2^2/mtilde^2]+6 Log[mE3^2/mtilde^2]+3 Log[mL1^2/mtilde^2]+3 Log[mL2^2/mtilde^2]+3 Log[mL3^2/mtilde^2]+Log[mQ1^2/mtilde^2]+Log[mQ2^2/mtilde^2]+Log[mQ3^2/mtilde^2]+8 Log[mU1^2/mtilde^2]+8 Log[mU2^2/mtilde^2]+8 Log[mU3^2/mtilde^2]) 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)+25 (Log[mL1^2/mtilde^2]+Log[mL2^2/mtilde^2]+Log[mL3^2/mtilde^2]+3 Log[mQ1^2/mtilde^2]+3 Log[mQ2^2/mtilde^2]+3 Log[mQ3^2/mtilde^2]) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))+3 Log[mU3^2/mtilde^2] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (2/5 Cos[2 ArcTan[tan\[Beta]]] 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))+3 Log[mQ3^2/mtilde^2] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (-(1/10) Cos[2 ArcTan[tan\[Beta]]] (\!\(
\*SubsuperscriptBox[\(g\), \(1\), \(2\)] - \(5\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)\))+
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))+(Xt^2 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\) (12 mQ3 mU3 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][mQ3/mU3]-Xt^2 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][mQ3/mU3]))/(2 mQ3^2 mU3^2)+(3 Xt^2 Cos[2 ArcTan[tan\[Beta]]] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 3][mQ3/mU3]+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 4][mQ3/mU3]))/(20 mQ3 mU3)-(Xt^2 Cos[2 ArcTan[tan\[Beta]]]^2 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 5][mQ3/mU3])/(4 mQ3 mU3)))


\[Lambda]HSS1lsuppressed[mtilde_,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=With[{factorfermions=91^2/Min[Abs@Q\[Mu],Abs@M2]^2,factorscalars=246^2/(mQ3 mU3)},1/4 91^2/mA^2 1/4 (3/5 Subscript[g, 1]^2+Subscript[g, 2]^2)Sin[4ArcTan[tan\[Beta]]]^2+1/(19200 \[Pi]^2) (factorfermions Abs@ (12 Cos[2 ArcTan[tan\[Beta]]]^2 gg[M1/Q\[Mu]] 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))+9 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\) (-22 Log[Q\[Mu]^2/mtilde^2]+2 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+f[M1/Q\[Mu]] (-31 Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-7 (3+Cos[4 ArcTan[tan\[Beta]]]) Subscript[f, 1][M1/Q\[Mu]]-9 Subscript[f, 3][M1/Q\[Mu]]+9 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 3][M1/Q\[Mu]])+25 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\) (6 (1+Cos[4 ArcTan[tan\[Beta]]]) gg[M2/Q\[Mu]]-8 Log[M2^2/mtilde^2]-8 Cos[4 ArcTan[tan\[Beta]]] Log[M2^2/mtilde^2]-82 Log[Q\[Mu]^2/mtilde^2]-10 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+3 f[M2/Q\[Mu]] (-31 Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-81 Subscript[f, 2][M2/Q\[Mu]]-27 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 2][M2/Q\[Mu]]-21 Subscript[f, 4][M2/Q\[Mu]]+21 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 4][M2/Q\[Mu]])+15 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) (6 (1+Cos[4 ArcTan[tan\[Beta]]]) gg[M2/Q\[Mu]]-24 Log[Q\[Mu]^2/mtilde^2]+24 Cos[4 ArcTan[tan\[Beta]]] Log[Q\[Mu]^2/mtilde^2]+3 f[M2/Q\[Mu]] Sin[2 ArcTan[tan\[Beta]]]+3 f[M2/Q\[Mu]] Sin[6 ArcTan[tan\[Beta]]]+f[M1/Q\[Mu]] (Sin[2 ArcTan[tan\[Beta]]]+Sin[6 ArcTan[tan\[Beta]]])-16 Subscript[f, 5][M1/Q\[Mu],M2/Q\[Mu]]+16 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 5][M1/Q\[Mu],M2/Q\[Mu]]-42 Subscript[f, 6][M1/Q\[Mu],M2/Q\[Mu]]-14 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 6][M1/Q\[Mu],M2/Q\[Mu]]-2 Subscript[f, 7][M1/Q\[Mu],M2/Q\[Mu]]+2 Cos[4 ArcTan[tan\[Beta]]] Subscript[f, 7][M1/Q\[Mu],M2/Q\[Mu]]-64 Sin[2 ArcTan[tan\[Beta]]] Subscript[f, 8][M1/Q\[Mu],M2/Q\[Mu]]))+1200 factorscalars Abs@(-(3/16) Sin[4 ArcTan[tan\[Beta]]]^2 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\))^2-1/4800 Log[mA^2/mtilde^2] (9 (-29+4 Cos[4 ArcTan[tan\[Beta]]]+9 Cos[8 ArcTan[tan\[Beta]]]) 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)-360 (5+3 Cos[4 ArcTan[tan\[Beta]]]) Sin[2 ArcTan[tan\[Beta]]]^2 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)+25 (-53+28 Cos[4 ArcTan[tan\[Beta]]]+9 Cos[8 ArcTan[tan\[Beta]]]) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))+1/300 Cos[2 ArcTan[tan\[Beta]]]^2 (3 (2 Log[mD1^2/mtilde^2]+2 Log[mD2^2/mtilde^2]+2 Log[mD3^2/mtilde^2]+6 Log[mE1^2/mtilde^2]+6 Log[mE2^2/mtilde^2]+6 Log[mE3^2/mtilde^2]+3 Log[mL1^2/mtilde^2]+3 Log[mL2^2/mtilde^2]+3 Log[mL3^2/mtilde^2]+Log[mQ1^2/mtilde^2]+Log[mQ2^2/mtilde^2]+Log[mQ3^2/mtilde^2]+8 Log[mU1^2/mtilde^2]+8 Log[mU2^2/mtilde^2]+8 Log[mU3^2/mtilde^2]) 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(4\)]\)+25 (Log[mL1^2/mtilde^2]+Log[mL2^2/mtilde^2]+Log[mL3^2/mtilde^2]+3 Log[mQ1^2/mtilde^2]+3 Log[mQ2^2/mtilde^2]+3 Log[mQ3^2/mtilde^2]) 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(4\)]\))+3 Log[mU3^2/mtilde^2] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (2/5 Cos[2 ArcTan[tan\[Beta]]] 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\)+
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))+3 Log[mQ3^2/mtilde^2] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (-(1/10) Cos[2 ArcTan[tan\[Beta]]] (\!\(
\*SubsuperscriptBox[\(g\), \(1\), \(2\)] - \(5\ 
\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)\))+
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))+(Xt^2 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\) (12 mQ3 mU3 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][mQ3/mU3]-Xt^2 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][mQ3/mU3]))/(2 mQ3^2 mU3^2)+(3 Xt^2 Cos[2 ArcTan[tan\[Beta]]] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) (3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 3][mQ3/mU3]+5 
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 4][mQ3/mU3]))/(20 mQ3 mU3)-(Xt^2 Cos[2 ArcTan[tan\[Beta]]]^2 ((3 
\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\))/5+
\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\)) 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\) Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 5][mQ3/mU3])/(4 mQ3 mU3)))]


(* ::Subsubsection::Closed:: *)
(*One loop O(Subscript[\[Alpha], b]) including tan\[Beta]-enhanced corrections*)


(* ::Text:: *)
(*The one-loop tan\[Beta]-enhanced SUSY threshold contribution to \[Lambda] from the sbottom is in \[Lambda]2lbottom[ ]. The factor Subscript[r, b] used in the Appendix of the paper is defined as gbDR[ ] cos\[Beta] / Subscript[g, b].*)


(* ::Text::Closed:: *)
(*Auxiliar*)


(* ::Input:: *)
(*\[Lambda]2lbottomaux:=1/(4\[Pi])^2 (6Subscript[g, b]^4) Subscript[X, b]^2/(mQ3 mD3) (Subscript[*)
(*\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][mQ3/mD3]-1/12 Subscript[X, b]^2/(mQ3 mD3) Subscript[*)
(*\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][mQ3/mD3])(1/(1-(4\[Pi])^-2 Subscript[\[CapitalDelta]h, b]))^4;*)
(*Subscript[\[CapitalDelta]h, b]:=8/3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)M3 Subscript[X, b] II[mQ3,mD3,M3]-Subscript[g, t]^2/Sin[ArcTan[tan\[Beta]]]^2 \[Mu] tan\[Beta] Subscript[X, t] II[mQ3,mU3,\[Mu]];*)


(* ::Input:: *)
(*\[Lambda]2lbottomaux/.{Subscript[X, b]->-\[Mu] tan\[Beta],Subscript[X, t]->Xt}*)


\[Lambda]2lbottom[mQ3_,mU3_,mD3_,M3_,\[Mu]_,tan\[Beta]_,Xt_]:=6/(16\[Pi]^2) (gbDR[mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt] Cos[ArcTan[tan\[Beta]]])^4 (tan\[Beta]^2 \[Mu]^2)/( mD3 mQ3 )  (Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][mQ3/mD3]-(tan\[Beta]^2 \[Mu]^2 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][mQ3/mD3])/(12 mD3 mQ3));
gbDR[mQ3_,mU3_,mD3_,M3_,\[Mu]_,tan\[Beta]_,Xt_]:=Subscript[g, b]/Cos[ArcTan[tan\[Beta]]] (1-(-(8/3) M3 tan\[Beta] \[Mu] II[mQ3,mD3,M3] 
\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\)-((1+tan\[Beta]^2) Xt \[Mu] II[mQ3,mU3,\[Mu]] 
\!\(\*SubsuperscriptBox[\(g\), \(t\), \(2\)]\))/tan\[Beta])/(16 \[Pi]^2))^-1;II[a_,b_,c_]:=Piecewise[{{1/(2a^2),Abs[a-b]<10^-2&&Abs[a-Abs[c]]<10^-2},{1/a^2 1/(1-(c/a)^2) (1+((c/a)^2 Log[(c/a)^2])/(1-(c/a)^2)),Abs[a-b]<10^-2},{-(1/a^2) 1/(1-(c/a)^2) (1+Log[(c/a)^2]/(1-(c/a)^2)),Abs[b-Abs[c]]<10^-2},{-(1/b^2) 1/(1-(c/b)^2) (1+Log[(c/b)^2]/(1-(c/b)^2)),Abs[a-Abs[c]]<10^-2}},(a^2 b^2 Log[a^2/b^2]+b^2 c^2 Log[b^2/c^2]+a^2 c^2 Log[c^2/a^2])/((a^2-b^2) (b^2-c^2) (a^2-c^2))]


(* ::Subsubsection::Closed:: *)
(*One loop O(Subscript[\[Alpha], \[Tau]]) including tan\[Beta]-enhanced corrections*)


(* ::Text:: *)
(*The one-loop tan\[Beta]-enhanced SUSY threshold contribution to \[Lambda] from the sbottom is in \[Lambda]2ltau[ ]. The factor Subscript[r, \[Tau]] used in the Appendix of the paper is defined as gtauDR[ ] cos\[Beta] / Subscript[g, \[Tau]].*)


\[Lambda]2ltau[mL3_,mE3_,M2_,M1_,\[Mu]_,tan\[Beta]_]:=(2/(16\[Pi]^2))(gtauDR[mL3,mE3,M2,M1,\[Mu],tan\[Beta]] Cos[ArcTan[tan\[Beta]]])^4 (tan\[Beta]^2 \[Mu]^2)/( mL3 mE3 )  (Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 1][mL3/mE3]-(tan\[Beta]^2 \[Mu]^2 Subscript[
\!\(\*OverscriptBox[\(F\), \(~\)]\), 2][mL3/mE3])/(12 mL3 mE3));
gtauDR[mL3_,mE3_,M2_,M1_,\[Mu]_,tan\[Beta]_]:=Subscript[g, \[Tau]]/Cos[ArcTan[tan\[Beta]]] (1-1/(4\[Pi])^2 tan\[Beta](Subscript[g, 2]^2 M2 \[Mu](II[mL3,M2,\[Mu]]+1/2 II[mL3,M2,\[Mu]])-3/5 Subscript[g, 1]^2 M1 (-\[Mu] II[mL3,mE3,M1]+1/2 \[Mu] II[mL3,M1,\[Mu]]-\[Mu] II[mE3,M1,\[Mu]])))^-1;


(* ::Subsection:: *)
(*Two - Loops*)


(* ::Subsubsection::Closed:: *)
(*Two - Loop O(Subscript[\[Alpha], t] Subscript[\[Alpha], S]) auxiliar manipulation*)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]2lstrongdegenerateaux:=1/(96 \[Pi]^4) g3^2 gt^4 (-Xth^5+Xth (-12-24 Log[Q^2/M3^2])+Xth^4 (1/2-Log[Q^2/M3^2])-18 Log[Q^2/M3^2]^2+Xth^3 (14+4 Log[Q^2/M3^2])+Xth^2 (-6+24 Log[Q^2/M3^2]))*)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]2lstrongaux:=1/(96 \[Pi]^4 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\) (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\))^2 (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\))^2) *)
(*\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\) (-9 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)-12 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)-18 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)]^2 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)+6 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)+18 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)-6 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)]^2 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)+6 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)+18 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)-6 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)-6 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)]^2 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(6\)]\)+27 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)+30 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)+36 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)]^2 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-15 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-36 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)+12 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)]^2 *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-15 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-36 Log[Q^2/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)+12 Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] Log[*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)/*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)] *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(6\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(4\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)+12 Log[*)
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(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\) (\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] - *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\))^4 (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\))^2 (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\))^2)+(\!\( *)
(*\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\ *)
(*\*SubsuperscriptBox[\(g\), \(t\), \(4\)]\ \((\(-2\)\ *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] + 2\ *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)] + Log[*)
(*\*FractionBox[*)
(*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)], *)
(*SubsuperscriptBox[\(M\), \(3\), \(2\)]]]\ \(( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)])\) - Log[*)
(*\*FractionBox[*)
(*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)], *)
(*SubsuperscriptBox[\(M\), \(3\), \(2\)]]]\ \(( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)])\))\)\ *)
(*\*SubscriptBox[\(M\), \(3\)]\ \((Log[*)
(*\*FractionBox[*)
(*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)], *)
(*SubsuperscriptBox[\(M\), \(3\), \(2\)]]]\ *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\ \(( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] - *)
(*\*SubsuperscriptBox[\(M\), \(3\), \(2\)])\) + Log[*)
(*\*FractionBox[*)
(*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)], *)
(*SubsuperscriptBox[\(M\), \(3\), \(2\)]]]\ *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\ \((\(-*)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\) + *)
(*\*SubsuperscriptBox[\(M\), \(3\), \(2\)])\))\)\ *)
(*\*SubsuperscriptBox[\(X\), \(t\), \(5\)]\))/(8 \[Pi]^4 (\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] - *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\))^4 (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)) (-*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)]\)+*)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)))*)


(* ::Subsubsection::Closed:: *)
(*Two - Loop O(Subscript[\[Alpha], t] Subscript[\[Alpha], S])*)


(* ::Text:: *)
(*The complete analytical expression for the two-loop O(Subscript[\[Alpha], t] Subscript[\[Alpha], s]) correction in the *)
(*\!\(\*OverscriptBox[\(DR\), \(_\)]\) scheme can be found in the definition of the function \[CapitalDelta]\[Lambda]2lstronggeneral[ ]. In the on-shell scheme one needs to add the shift contribution given in the function shiftDROS\[Alpha]t\[Alpha]Sgeneral[ ].*)


\[CapitalDelta]\[Lambda]2lstrong[mtilde_,mQ3_,mU3_,Xt_,M3_]:=Subscript[g, 3]^2 Subscript[g, t]^4 With[{\[Delta]=8 10^-2,\[Delta]2=1 10^-2},Piecewise[{{\[CapitalDelta]\[Lambda]2lstrongdegenerate[mtilde,mQ3,Xt],Abs[mQ3/mU3-1]<\[Delta]2&&Abs[M3/mU3-1]<\[Delta]2&&Abs[M3/mQ3-1]<\[Delta]2},{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mU3(1+\[Delta]),mU3,Xt ,M3]] (mQ3-mU3(1-\[Delta]))/(2mU3 \[Delta])+Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mU3(1-\[Delta]),mU3,Xt ,M3]](1-(mQ3-mU3(1-\[Delta]))/(2 mU3 \[Delta])),Abs[mQ3/mU3-1]<= \[Delta]},
{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mQ3,mU3,Xt ,mQ3(1+\[Delta])]] (M3-mQ3(1-\[Delta]))/(2mQ3 \[Delta])+Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mQ3,mU3,Xt ,mQ3(1-\[Delta])]](1-(M3-mQ3(1-\[Delta]))/(2mQ3 \[Delta])),Abs[mQ3/M3-1]<=\[Delta]},
{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mQ3,mU3,Xt ,mU3(1+\[Delta])]] (M3-mU3(1-\[Delta]))/(2mU3 \[Delta])+Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.mtilde,mQ3,mU3,Xt ,mU3(1-\[Delta])]](1-(M3-mU3(1-\[Delta]))/(2mU3 \[Delta])),Abs[mU3/M3-1]<= \[Delta]}},Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,1.mQ3,mU3,Xt ,M3]]]]
(*The two loop corrections has singularities for mQ3\[Rule]mU3, mU3\[Rule]M3 and mQ3\[Rule]mU3. We avoid evaluating the function at the singular points by using a linear interpolation near the singular point, i.e. for |x-Subscript[x, 0]|<\[Delta].*)


(* ::Input::Closed:: *)
(*(*commented:old definition*)*)


(* ::Input:: *)
(*(*\[CapitalDelta]\[Lambda]2lstrong[mtilde_,mQ3_,mU3_,Xt_,M3_]:=Subscript[g, 3]^2Subscript[g, t]^4Piecewise[{{\[CapitalDelta]\[Lambda]2lstrongdegenerate[mtilde,M3,Xt],Abs[mQ3/mU3-1]<3. 10^-2&&Abs[M3/mU3-1]<3. 10^-2&&Abs[M3/mQ3-1]<3. 10^-2},{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,1.01mQ3,mU3,Xt ,M3]],Abs[mQ3/mU3-1]< 10^-2},*)
(*{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,1.01mQ3,mU3,Xt ,M3]],Abs[mQ3/M3-1]< 10^-2},*)
(*{Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,mQ3,1.01mU3,Xt ,M3]],Abs[mU3/M3-1]< 10^-2}},Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,1.mQ3,mU3,Xt ,M3]]]*)*)


(* ::Input:: *)
(*(*\[CapitalDelta]\[Lambda]2lstrong[mtilde_,mQ3_,mU3_,Xt_,M3_]:=*)
(*Subscript[g, 3]^2Subscript[g, t]^4If[Abs[mQ3/mU3-1]<10^-2&&Abs[M3/mU3-1]<10^-2&&Abs[M3/mQ3-1]<10^-2,*)
(*\[CapitalDelta]\[Lambda]2lstrongdegenerate[mtilde,M3,Xt],*)
(*If[Abs[mQ3/mU3-1]<10^-2||Abs[M3/mU3-1]<10^-2||Abs[M3/mQ3-1]<10^-2,*)
(*	Re[\[CapitalDelta]\[Lambda]2lstronggeneral[1.013mtilde,mQ3,1.011mU3,Xt ,1.012M3]],*)
(*	Re[\[CapitalDelta]\[Lambda]2lstronggeneral[mtilde,1.mQ3,mU3,Xt ,M3]]]*)
(*]*)*)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]2lstrongdegenerateaux/.{Xth->Xt/M3,g3->1,gt->1}*)


\[CapitalDelta]\[Lambda]2lstrongdegenerate[Q_,M3_,Xt_]:=1/(96 \[Pi]^4) (-(Xt^5/M3^5)+(Xt (-12-24 Log[Q^2/M3^2]))/M3+(Xt^4 (1/2-Log[Q^2/M3^2]))/M3^4-18 Log[Q^2/M3^2]^2+(Xt^3 (14+4 Log[Q^2/M3^2]))/M3^3+(Xt^2 (-6+24 Log[Q^2/M3^2]))/M3^2)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]2lstrongaux/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt,*)
(*\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[g, 3]->1,Subscript[g, t]->1}*)


\[CapitalDelta]\[Lambda]2lstronggeneral[Q_,mQ3_,mU3_,Xt_,M3_]:=(M3 Xt^5 (mQ3^2 (M3^2-mU3^2) Log[mQ3^2/M3^2]+(-M3^2+mQ3^2) mU3^2 Log[mU3^2/M3^2]) (-2 mQ3^2+2 mU3^2+(mQ3^2+mU3^2) Log[mQ3^2/M3^2]-(mQ3^2+mU3^2) Log[mU3^2/M3^2]))/(8 (M3^2-mQ3^2) (M3^2-mU3^2) (mQ3^2-mU3^2)^4 \[Pi]^4)-(Xt^2 (mQ3^2 mU3^2 (M3^2-mU3^2)^2 (4 mQ3^6-2 mQ3^4 mU3^2+M3^4 (3 mQ3^2-mU3^2)+M3^2 (-8 mQ3^4+4 mQ3^2 mU3^2)) Log[mQ3^2/M3^2]^2+(M3^2-mQ3^2) (mQ3^2 mU3^2 (-M3^6 (mQ3^2-3 mU3^2)+2 mQ3^2 mU3^4 (mQ3^2-2 mU3^2)+M3^4 (mQ3^4+mQ3^2 mU3^2-8 mU3^4)+M3^2 (-4 mQ3^4 mU3^2+6 mQ3^2 mU3^4+4 mU3^6)) Log[mU3^2/M3^2]^2+2 M3^2 (M3^2-mQ3^2) (M3^2-mU3^2)^2 (mQ3^2-mU3^2)^2 (1+Log[Q^2/M3^2])-mQ3^2 mU3^2 (mQ3^2-mU3^2) (-M3^2+mU3^2) Log[mU3^2/M3^2] (7 M3^4+3 mQ3^2 mU3^2-2 M3^2 (3 mQ3^2+2 mU3^2)+6 (M3^2-mQ3^2) (M3^2-mU3^2) Log[Q^2/M3^2]))+mQ3^2 mU3^2 Log[mQ3^2/M3^2] ((-2 M3^8 (mQ3^2+mU3^2)-2 mQ3^4 mU3^4 (mQ3^2+mU3^2)+4 M3^2 mQ3^2 mU3^2 (mQ3^2+mU3^2)^2-3 M3^4 (mQ3^2+mU3^2)^3+2 M3^6 (3 mQ3^4+2 mQ3^2 mU3^2+3 mU3^4)) Log[mU3^2/M3^2]-(M3^2-mQ3^2) (M3^2-mU3^2) (mQ3^2-mU3^2) (7 M3^4+3 mQ3^2 mU3^2-2 M3^2 (2 mQ3^2+3 mU3^2)+6 (M3^2-mQ3^2) (M3^2-mU3^2) Log[Q^2/M3^2]))))/(16 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 (M3^2-mU3^2)^2 (mQ3^2-mU3^2)^2 \[Pi]^4)+(M3 Xt (2 M3^2 mQ3^2 \[Pi]^2-2 M3^2 mU3^2 \[Pi]^2-6 M3^4 Log[mQ3^2/M3^2]+6 M3^2 mQ3^2 Log[mQ3^2/M3^2]+6 M3^2 mU3^2 Log[mQ3^2/M3^2]-6 mQ3^2 mU3^2 Log[mQ3^2/M3^2]+6 M3^4 Log[mQ3^2/M3^2]^2-3 M3^2 mQ3^2 Log[mQ3^2/M3^2]^2-6 M3^2 mU3^2 Log[mQ3^2/M3^2]^2+3 mQ3^2 mU3^2 Log[mQ3^2/M3^2]^2-12 M3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+12 M3^2 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+6 M3^4 Log[mU3^2/M3^2]-6 M3^2 mQ3^2 Log[mU3^2/M3^2]-6 M3^2 mU3^2 Log[mU3^2/M3^2]+6 mQ3^2 mU3^2 Log[mU3^2/M3^2]-3 M3^2 mQ3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+3 M3^2 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-6 M3^4 Log[mU3^2/M3^2]^2+6 M3^2 mQ3^2 Log[mU3^2/M3^2]^2+3 M3^2 mU3^2 Log[mU3^2/M3^2]^2-3 mQ3^2 mU3^2 Log[mU3^2/M3^2]^2+12 M3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-12 M3^2 mQ3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-6 M3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+6 M3^2 mQ3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+6 M3^2 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-6 mQ3^2 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+6 M3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-6 M3^2 mQ3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-6 M3^2 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+6 mQ3^2 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-12 (M3^4-M3^2 mU3^2) PolyLog[2,M3^2/mQ3^2]+12 (M3^4-M3^2 mQ3^2) PolyLog[2,M3^2/mU3^2]))/(24 (M3^2-mQ3^2) (M3^2-mU3^2) (mQ3^2-mU3^2) \[Pi]^4)+(6 M3^10 mQ3^2-12 M3^8 mQ3^4+6 M3^6 mQ3^6+6 M3^10 mU3^2-39 M3^8 mQ3^2 mU3^2+57 M3^6 mQ3^4 mU3^2-24 M3^4 mQ3^6 mU3^2-12 M3^8 mU3^4+57 M3^6 mQ3^2 mU3^4-72 M3^4 mQ3^4 mU3^4+27 M3^2 mQ3^6 mU3^4+6 M3^6 mU3^6-24 M3^4 mQ3^2 mU3^6+27 M3^2 mQ3^4 mU3^6-9 mQ3^6 mU3^6-4 M3^8 mQ3^2 mU3^2 \[Pi]^2+4 M3^6 mQ3^4 mU3^2 \[Pi]^2-2 M3^4 mQ3^6 mU3^2 \[Pi]^2+4 M3^6 mQ3^2 mU3^4 \[Pi]^2-2 M3^4 mQ3^2 mU3^6 \[Pi]^2+21 M3^8 mQ3^2 mU3^2 Log[mQ3^2/M3^2]-21 M3^6 mQ3^4 mU3^2 Log[mQ3^2/M3^2]+9 M3^4 mQ3^6 mU3^2 Log[mQ3^2/M3^2]-39 M3^6 mQ3^2 mU3^4 Log[mQ3^2/M3^2]+36 M3^4 mQ3^4 mU3^4 Log[mQ3^2/M3^2]-15 M3^2 mQ3^6 mU3^4 Log[mQ3^2/M3^2]+18 M3^4 mQ3^2 mU3^6 Log[mQ3^2/M3^2]-15 M3^2 mQ3^4 mU3^6 Log[mQ3^2/M3^2]+6 mQ3^6 mU3^6 Log[mQ3^2/M3^2]-9 M3^8 mQ3^2 mU3^2 Log[mQ3^2/M3^2]^2+12 M3^6 mQ3^4 mU3^2 Log[mQ3^2/M3^2]^2-6 M3^4 mQ3^6 mU3^2 Log[mQ3^2/M3^2]^2+18 M3^6 mQ3^2 mU3^4 Log[mQ3^2/M3^2]^2-24 M3^4 mQ3^4 mU3^4 Log[mQ3^2/M3^2]^2+12 M3^2 mQ3^6 mU3^4 Log[mQ3^2/M3^2]^2-9 M3^4 mQ3^2 mU3^6 Log[mQ3^2/M3^2]^2+12 M3^2 mQ3^4 mU3^6 Log[mQ3^2/M3^2]^2-6 mQ3^6 mU3^6 Log[mQ3^2/M3^2]^2+12 M3^8 mQ3^2 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-24 M3^6 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+12 M3^4 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+21 M3^8 mQ3^2 mU3^2 Log[mU3^2/M3^2]-39 M3^6 mQ3^4 mU3^2 Log[mU3^2/M3^2]+18 M3^4 mQ3^6 mU3^2 Log[mU3^2/M3^2]-21 M3^6 mQ3^2 mU3^4 Log[mU3^2/M3^2]+36 M3^4 mQ3^4 mU3^4 Log[mU3^2/M3^2]-15 M3^2 mQ3^6 mU3^4 Log[mU3^2/M3^2]+9 M3^4 mQ3^2 mU3^6 Log[mU3^2/M3^2]-15 M3^2 mQ3^4 mU3^6 Log[mU3^2/M3^2]+6 mQ3^6 mU3^6 Log[mU3^2/M3^2]+6 M3^6 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-3 M3^4 mQ3^6 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+6 M3^6 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-24 M3^4 mQ3^4 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+12 M3^2 mQ3^6 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-3 M3^4 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+12 M3^2 mQ3^4 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-6 mQ3^6 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-9 M3^8 mQ3^2 mU3^2 Log[mU3^2/M3^2]^2+18 M3^6 mQ3^4 mU3^2 Log[mU3^2/M3^2]^2-9 M3^4 mQ3^6 mU3^2 Log[mU3^2/M3^2]^2+12 M3^6 mQ3^2 mU3^4 Log[mU3^2/M3^2]^2-24 M3^4 mQ3^4 mU3^4 Log[mU3^2/M3^2]^2+12 M3^2 mQ3^6 mU3^4 Log[mU3^2/M3^2]^2-6 M3^4 mQ3^2 mU3^6 Log[mU3^2/M3^2]^2+12 M3^2 mQ3^4 mU3^6 Log[mU3^2/M3^2]^2-6 mQ3^6 mU3^6 Log[mU3^2/M3^2]^2+12 M3^8 mQ3^2 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-24 M3^6 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+12 M3^4 mQ3^6 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+6 M3^10 mQ3^2 Log[Q^2/M3^2]-12 M3^8 mQ3^4 Log[Q^2/M3^2]+6 M3^6 mQ3^6 Log[Q^2/M3^2]+6 M3^10 mU3^2 Log[Q^2/M3^2]-36 M3^8 mQ3^2 mU3^2 Log[Q^2/M3^2]+54 M3^6 mQ3^4 mU3^2 Log[Q^2/M3^2]-24 M3^4 mQ3^6 mU3^2 Log[Q^2/M3^2]-12 M3^8 mU3^4 Log[Q^2/M3^2]+54 M3^6 mQ3^2 mU3^4 Log[Q^2/M3^2]-72 M3^4 mQ3^4 mU3^4 Log[Q^2/M3^2]+30 M3^2 mQ3^6 mU3^4 Log[Q^2/M3^2]+6 M3^6 mU3^6 Log[Q^2/M3^2]-24 M3^4 mQ3^2 mU3^6 Log[Q^2/M3^2]+30 M3^2 mQ3^4 mU3^6 Log[Q^2/M3^2]-12 mQ3^6 mU3^6 Log[Q^2/M3^2]+18 M3^8 mQ3^2 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-36 M3^6 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+18 M3^4 mQ3^6 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-36 M3^6 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+72 M3^4 mQ3^4 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-36 M3^2 mQ3^6 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+18 M3^4 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-36 M3^2 mQ3^4 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+18 mQ3^6 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+18 M3^8 mQ3^2 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-36 M3^6 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+18 M3^4 mQ3^6 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-36 M3^6 mQ3^2 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]+72 M3^4 mQ3^4 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-36 M3^2 mQ3^6 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]+18 M3^4 mQ3^2 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]-36 M3^2 mQ3^4 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]+18 mQ3^6 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]-18 M3^8 mQ3^2 mU3^2 Log[Q^2/M3^2]^2+36 M3^6 mQ3^4 mU3^2 Log[Q^2/M3^2]^2-18 M3^4 mQ3^6 mU3^2 Log[Q^2/M3^2]^2+36 M3^6 mQ3^2 mU3^4 Log[Q^2/M3^2]^2-72 M3^4 mQ3^4 mU3^4 Log[Q^2/M3^2]^2+36 M3^2 mQ3^6 mU3^4 Log[Q^2/M3^2]^2-18 M3^4 mQ3^2 mU3^6 Log[Q^2/M3^2]^2+36 M3^2 mQ3^4 mU3^6 Log[Q^2/M3^2]^2-18 mQ3^6 mU3^6 Log[Q^2/M3^2]^2+12 M3^4 mQ3^2 mU3^2 (M3^2-mU3^2)^2 PolyLog[2,M3^2/mQ3^2]+12 M3^4 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 PolyLog[2,M3^2/mU3^2])/(96 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 (M3^2-mU3^2)^2 \[Pi]^4)+(M3 Xt^3 (-8 M3^4 mQ3^2+8 M3^2 mQ3^4+8 M3^4 mU3^2-8 mQ3^4 mU3^2-8 M3^2 mU3^4+8 mQ3^2 mU3^4+6 M3^4 mQ3^2 Log[mQ3^2/M3^2]-6 M3^2 mQ3^4 Log[mQ3^2/M3^2]+2 M3^4 mU3^2 Log[mQ3^2/M3^2]-8 M3^2 mQ3^2 mU3^2 Log[mQ3^2/M3^2]+6 mQ3^4 mU3^2 Log[mQ3^2/M3^2]-2 M3^2 mU3^4 Log[mQ3^2/M3^2]+2 mQ3^2 mU3^4 Log[mQ3^2/M3^2]+2 M3^6 Log[mQ3^2/M3^2]^2-3 M3^4 mQ3^2 Log[mQ3^2/M3^2]^2-M3^2 mQ3^4 Log[mQ3^2/M3^2]^2-3 M3^4 mU3^2 Log[mQ3^2/M3^2]^2+6 M3^2 mQ3^2 mU3^2 Log[mQ3^2/M3^2]^2+mQ3^4 mU3^2 Log[mQ3^2/M3^2]^2+M3^2 mU3^4 Log[mQ3^2/M3^2]^2-3 mQ3^2 mU3^4 Log[mQ3^2/M3^2]^2-4 M3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+6 M3^4 mQ3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-2 M3^2 mQ3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+6 M3^4 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-8 M3^2 mQ3^2 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+2 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-2 M3^2 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+2 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-2 M3^4 mQ3^2 Log[mU3^2/M3^2]+2 M3^2 mQ3^4 Log[mU3^2/M3^2]-6 M3^4 mU3^2 Log[mU3^2/M3^2]+8 M3^2 mQ3^2 mU3^2 Log[mU3^2/M3^2]-2 mQ3^4 mU3^2 Log[mU3^2/M3^2]+6 M3^2 mU3^4 Log[mU3^2/M3^2]-6 mQ3^2 mU3^4 Log[mU3^2/M3^2]+2 M3^2 mQ3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-4 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-2 M3^2 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+4 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-2 M3^6 Log[mU3^2/M3^2]^2+3 M3^4 mQ3^2 Log[mU3^2/M3^2]^2-M3^2 mQ3^4 Log[mU3^2/M3^2]^2+3 M3^4 mU3^2 Log[mU3^2/M3^2]^2-6 M3^2 mQ3^2 mU3^2 Log[mU3^2/M3^2]^2+3 mQ3^4 mU3^2 Log[mU3^2/M3^2]^2+M3^2 mU3^4 Log[mU3^2/M3^2]^2-mQ3^2 mU3^4 Log[mU3^2/M3^2]^2+4 M3^6 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-6 M3^4 mQ3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+2 M3^2 mQ3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-6 M3^4 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+8 M3^2 mQ3^2 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-2 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+2 M3^2 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-2 mQ3^2 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-4 M3^4 mQ3^2 Log[Q^2/M3^2]+4 M3^2 mQ3^4 Log[Q^2/M3^2]+4 M3^4 mU3^2 Log[Q^2/M3^2]-4 mQ3^4 mU3^2 Log[Q^2/M3^2]-4 M3^2 mU3^4 Log[Q^2/M3^2]+4 mQ3^2 mU3^4 Log[Q^2/M3^2]+2 M3^4 mQ3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-2 M3^2 mQ3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+2 M3^4 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-4 M3^2 mQ3^2 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+2 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-2 M3^2 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+2 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-2 M3^4 mQ3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+2 M3^2 mQ3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 M3^4 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+4 M3^2 mQ3^2 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+2 M3^2 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 mQ3^2 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 (M3^2-mQ3^2) (M3^2-mU3^2) (2 M3^2-mQ3^2-mU3^2) PolyLog[2,M3^2/mQ3^2]+2 (M3^2-mQ3^2) (M3^2-mU3^2) (2 M3^2-mQ3^2-mU3^2) PolyLog[2,M3^2/mU3^2]))/(8 (M3^2-mQ3^2) (M3^2-mU3^2) (mQ3^2-mU3^2)^3 \[Pi]^4)+(Xt^4 (2 M3^10 mQ3^6-4 M3^8 mQ3^8+2 M3^6 mQ3^10-2 M3^10 mQ3^4 mU3^2+14 M3^8 mQ3^6 mU3^2-20 M3^6 mQ3^8 mU3^2+8 M3^4 mQ3^10 mU3^2-2 M3^10 mQ3^2 mU3^4-20 M3^8 mQ3^4 mU3^4+18 M3^6 mQ3^6 mU3^4+24 M3^4 mQ3^8 mU3^4-20 M3^2 mQ3^10 mU3^4+2 M3^10 mU3^6+14 M3^8 mQ3^2 mU3^6+18 M3^6 mQ3^4 mU3^6-64 M3^4 mQ3^6 mU3^6+20 M3^2 mQ3^8 mU3^6+10 mQ3^10 mU3^6-4 M3^8 mU3^8-20 M3^6 mQ3^2 mU3^8+24 M3^4 mQ3^4 mU3^8+20 M3^2 mQ3^6 mU3^8-20 mQ3^8 mU3^8+2 M3^6 mU3^10+8 M3^4 mQ3^2 mU3^10-20 M3^2 mQ3^4 mU3^10+10 mQ3^6 mU3^10-4 M3^10 mQ3^4 mU3^2 Log[mQ3^2/M3^2]-7 M3^8 mQ3^6 mU3^2 Log[mQ3^2/M3^2]+29 M3^6 mQ3^8 mU3^2 Log[mQ3^2/M3^2]-16 M3^4 mQ3^10 mU3^2 Log[mQ3^2/M3^2]+4 M3^10 mQ3^2 mU3^4 Log[mQ3^2/M3^2]+8 M3^8 mQ3^4 mU3^4 Log[mQ3^2/M3^2]-7 M3^6 mQ3^6 mU3^4 Log[mQ3^2/M3^2]-44 M3^4 mQ3^8 mU3^4 Log[mQ3^2/M3^2]+31 M3^2 mQ3^10 mU3^4 Log[mQ3^2/M3^2]-M3^8 mQ3^2 mU3^6 Log[mQ3^2/M3^2]-13 M3^6 mQ3^4 mU3^6 Log[mQ3^2/M3^2]+38 M3^4 mQ3^6 mU3^6 Log[mQ3^2/M3^2]+3 M3^2 mQ3^8 mU3^6 Log[mQ3^2/M3^2]-15 mQ3^10 mU3^6 Log[mQ3^2/M3^2]-9 M3^6 mQ3^2 mU3^8 Log[mQ3^2/M3^2]+16 M3^4 mQ3^4 mU3^8 Log[mQ3^2/M3^2]-27 M3^2 mQ3^6 mU3^8 Log[mQ3^2/M3^2]+12 mQ3^8 mU3^8 Log[mQ3^2/M3^2]+6 M3^4 mQ3^2 mU3^10 Log[mQ3^2/M3^2]-7 M3^2 mQ3^4 mU3^10 Log[mQ3^2/M3^2]+3 mQ3^6 mU3^10 Log[mQ3^2/M3^2]+2 M3^10 mQ3^4 mU3^2 Log[mQ3^2/M3^2]^2-8 M3^6 mQ3^8 mU3^2 Log[mQ3^2/M3^2]^2+5 M3^4 mQ3^10 mU3^2 Log[mQ3^2/M3^2]^2-2 M3^10 mQ3^2 mU3^4 Log[mQ3^2/M3^2]^2+4 M3^8 mQ3^4 mU3^4 Log[mQ3^2/M3^2]^2-10 M3^6 mQ3^6 mU3^4 Log[mQ3^2/M3^2]^2+20 M3^4 mQ3^8 mU3^4 Log[mQ3^2/M3^2]^2-10 M3^2 mQ3^10 mU3^4 Log[mQ3^2/M3^2]^2+4 M3^8 mQ3^2 mU3^6 Log[mQ3^2/M3^2]^2-12 M3^6 mQ3^4 mU3^6 Log[mQ3^2/M3^2]^2+19 M3^4 mQ3^6 mU3^6 Log[mQ3^2/M3^2]^2-16 M3^2 mQ3^8 mU3^6 Log[mQ3^2/M3^2]^2+5 mQ3^10 mU3^6 Log[mQ3^2/M3^2]^2-2 M3^6 mQ3^2 mU3^8 Log[mQ3^2/M3^2]^2+4 M3^4 mQ3^4 mU3^8 Log[mQ3^2/M3^2]^2-8 M3^2 mQ3^6 mU3^8 Log[mQ3^2/M3^2]^2+4 mQ3^8 mU3^8 Log[mQ3^2/M3^2]^2+2 M3^2 mQ3^4 mU3^10 Log[mQ3^2/M3^2]^2-mQ3^6 mU3^10 Log[mQ3^2/M3^2]^2-4 M3^10 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+10 M3^8 mQ3^6 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-8 M3^6 mQ3^8 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+2 M3^4 mQ3^10 mU3^2 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+4 M3^10 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-16 M3^6 mQ3^6 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+16 M3^4 mQ3^8 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-4 M3^2 mQ3^10 mU3^4 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-10 M3^8 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+16 M3^6 mQ3^4 mU3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-8 M3^2 mQ3^8 mU3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+2 mQ3^10 mU3^6 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+8 M3^6 mQ3^2 mU3^8 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-16 M3^4 mQ3^4 mU3^8 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+8 M3^2 mQ3^6 mU3^8 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-2 M3^4 mQ3^2 mU3^10 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+4 M3^2 mQ3^4 mU3^10 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]-2 mQ3^6 mU3^10 Log[mQ3^2/M3^2] Log[mQ3^2/(-M3^2+mQ3^2)]+4 M3^10 mQ3^4 mU3^2 Log[mU3^2/M3^2]-M3^8 mQ3^6 mU3^2 Log[mU3^2/M3^2]-9 M3^6 mQ3^8 mU3^2 Log[mU3^2/M3^2]+6 M3^4 mQ3^10 mU3^2 Log[mU3^2/M3^2]-4 M3^10 mQ3^2 mU3^4 Log[mU3^2/M3^2]+8 M3^8 mQ3^4 mU3^4 Log[mU3^2/M3^2]-13 M3^6 mQ3^6 mU3^4 Log[mU3^2/M3^2]+16 M3^4 mQ3^8 mU3^4 Log[mU3^2/M3^2]-7 M3^2 mQ3^10 mU3^4 Log[mU3^2/M3^2]-7 M3^8 mQ3^2 mU3^6 Log[mU3^2/M3^2]-7 M3^6 mQ3^4 mU3^6 Log[mU3^2/M3^2]+38 M3^4 mQ3^6 mU3^6 Log[mU3^2/M3^2]-27 M3^2 mQ3^8 mU3^6 Log[mU3^2/M3^2]+3 mQ3^10 mU3^6 Log[mU3^2/M3^2]+29 M3^6 mQ3^2 mU3^8 Log[mU3^2/M3^2]-44 M3^4 mQ3^4 mU3^8 Log[mU3^2/M3^2]+3 M3^2 mQ3^6 mU3^8 Log[mU3^2/M3^2]+12 mQ3^8 mU3^8 Log[mU3^2/M3^2]-16 M3^4 mQ3^2 mU3^10 Log[mU3^2/M3^2]+31 M3^2 mQ3^4 mU3^10 Log[mU3^2/M3^2]-15 mQ3^6 mU3^10 Log[mU3^2/M3^2]-4 M3^8 mQ3^6 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+10 M3^6 mQ3^8 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-5 M3^4 mQ3^10 mU3^2 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-8 M3^8 mQ3^4 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+22 M3^6 mQ3^6 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-24 M3^4 mQ3^8 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+8 M3^2 mQ3^10 mU3^4 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-4 M3^8 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+22 M3^6 mQ3^4 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-38 M3^4 mQ3^6 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+24 M3^2 mQ3^8 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-4 mQ3^10 mU3^6 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+10 M3^6 mQ3^2 mU3^8 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-24 M3^4 mQ3^4 mU3^8 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+24 M3^2 mQ3^6 mU3^8 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-8 mQ3^8 mU3^8 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-5 M3^4 mQ3^2 mU3^10 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]+8 M3^2 mQ3^4 mU3^10 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-4 mQ3^6 mU3^10 Log[mQ3^2/M3^2] Log[mU3^2/M3^2]-2 M3^10 mQ3^4 mU3^2 Log[mU3^2/M3^2]^2+4 M3^8 mQ3^6 mU3^2 Log[mU3^2/M3^2]^2-2 M3^6 mQ3^8 mU3^2 Log[mU3^2/M3^2]^2+2 M3^10 mQ3^2 mU3^4 Log[mU3^2/M3^2]^2+4 M3^8 mQ3^4 mU3^4 Log[mU3^2/M3^2]^2-12 M3^6 mQ3^6 mU3^4 Log[mU3^2/M3^2]^2+4 M3^4 mQ3^8 mU3^4 Log[mU3^2/M3^2]^2+2 M3^2 mQ3^10 mU3^4 Log[mU3^2/M3^2]^2-10 M3^6 mQ3^4 mU3^6 Log[mU3^2/M3^2]^2+19 M3^4 mQ3^6 mU3^6 Log[mU3^2/M3^2]^2-8 M3^2 mQ3^8 mU3^6 Log[mU3^2/M3^2]^2-mQ3^10 mU3^6 Log[mU3^2/M3^2]^2-8 M3^6 mQ3^2 mU3^8 Log[mU3^2/M3^2]^2+20 M3^4 mQ3^4 mU3^8 Log[mU3^2/M3^2]^2-16 M3^2 mQ3^6 mU3^8 Log[mU3^2/M3^2]^2+4 mQ3^8 mU3^8 Log[mU3^2/M3^2]^2+5 M3^4 mQ3^2 mU3^10 Log[mU3^2/M3^2]^2-10 M3^2 mQ3^4 mU3^10 Log[mU3^2/M3^2]^2+5 mQ3^6 mU3^10 Log[mU3^2/M3^2]^2+4 M3^10 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-10 M3^8 mQ3^6 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+8 M3^6 mQ3^8 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-2 M3^4 mQ3^10 mU3^2 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-4 M3^10 mQ3^2 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+16 M3^6 mQ3^6 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-16 M3^4 mQ3^8 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+4 M3^2 mQ3^10 mU3^4 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+10 M3^8 mQ3^2 mU3^6 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-16 M3^6 mQ3^4 mU3^6 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+8 M3^2 mQ3^8 mU3^6 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-2 mQ3^10 mU3^6 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-8 M3^6 mQ3^2 mU3^8 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+16 M3^4 mQ3^4 mU3^8 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-8 M3^2 mQ3^6 mU3^8 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+2 M3^4 mQ3^2 mU3^10 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]-4 M3^2 mQ3^4 mU3^10 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+2 mQ3^6 mU3^10 Log[mU3^2/M3^2] Log[mU3^2/(-M3^2+mU3^2)]+2 M3^10 mQ3^6 Log[Q^2/M3^2]-4 M3^8 mQ3^8 Log[Q^2/M3^2]+2 M3^6 mQ3^10 Log[Q^2/M3^2]-2 M3^10 mQ3^4 mU3^2 Log[Q^2/M3^2]+12 M3^8 mQ3^6 mU3^2 Log[Q^2/M3^2]-18 M3^6 mQ3^8 mU3^2 Log[Q^2/M3^2]+8 M3^4 mQ3^10 mU3^2 Log[Q^2/M3^2]-2 M3^10 mQ3^2 mU3^4 Log[Q^2/M3^2]-16 M3^8 mQ3^4 mU3^4 Log[Q^2/M3^2]+16 M3^6 mQ3^6 mU3^4 Log[Q^2/M3^2]+24 M3^4 mQ3^8 mU3^4 Log[Q^2/M3^2]-22 M3^2 mQ3^10 mU3^4 Log[Q^2/M3^2]+2 M3^10 mU3^6 Log[Q^2/M3^2]+12 M3^8 mQ3^2 mU3^6 Log[Q^2/M3^2]+16 M3^6 mQ3^4 mU3^6 Log[Q^2/M3^2]-64 M3^4 mQ3^6 mU3^6 Log[Q^2/M3^2]+22 M3^2 mQ3^8 mU3^6 Log[Q^2/M3^2]+12 mQ3^10 mU3^6 Log[Q^2/M3^2]-4 M3^8 mU3^8 Log[Q^2/M3^2]-18 M3^6 mQ3^2 mU3^8 Log[Q^2/M3^2]+24 M3^4 mQ3^4 mU3^8 Log[Q^2/M3^2]+22 M3^2 mQ3^6 mU3^8 Log[Q^2/M3^2]-24 mQ3^8 mU3^8 Log[Q^2/M3^2]+2 M3^6 mU3^10 Log[Q^2/M3^2]+8 M3^4 mQ3^2 mU3^10 Log[Q^2/M3^2]-22 M3^2 mQ3^4 mU3^10 Log[Q^2/M3^2]+12 mQ3^6 mU3^10 Log[Q^2/M3^2]-4 M3^10 mQ3^4 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+2 M3^8 mQ3^6 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+8 M3^6 mQ3^8 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-6 M3^4 mQ3^10 mU3^2 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+4 M3^10 mQ3^2 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-16 M3^4 mQ3^8 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+12 M3^2 mQ3^10 mU3^4 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-2 M3^8 mQ3^2 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+8 M3^2 mQ3^8 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-6 mQ3^10 mU3^6 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-8 M3^6 mQ3^2 mU3^8 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+16 M3^4 mQ3^4 mU3^8 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-8 M3^2 mQ3^6 mU3^8 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+6 M3^4 mQ3^2 mU3^10 Log[mQ3^2/M3^2] Log[Q^2/M3^2]-12 M3^2 mQ3^4 mU3^10 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+6 mQ3^6 mU3^10 Log[mQ3^2/M3^2] Log[Q^2/M3^2]+4 M3^10 mQ3^4 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 M3^8 mQ3^6 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-8 M3^6 mQ3^8 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]+6 M3^4 mQ3^10 mU3^2 Log[mU3^2/M3^2] Log[Q^2/M3^2]-4 M3^10 mQ3^2 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]+16 M3^4 mQ3^8 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]-12 M3^2 mQ3^10 mU3^4 Log[mU3^2/M3^2] Log[Q^2/M3^2]+2 M3^8 mQ3^2 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]-8 M3^2 mQ3^8 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]+6 mQ3^10 mU3^6 Log[mU3^2/M3^2] Log[Q^2/M3^2]+8 M3^6 mQ3^2 mU3^8 Log[mU3^2/M3^2] Log[Q^2/M3^2]-16 M3^4 mQ3^4 mU3^8 Log[mU3^2/M3^2] Log[Q^2/M3^2]+8 M3^2 mQ3^6 mU3^8 Log[mU3^2/M3^2] Log[Q^2/M3^2]-6 M3^4 mQ3^2 mU3^10 Log[mU3^2/M3^2] Log[Q^2/M3^2]+12 M3^2 mQ3^4 mU3^10 Log[mU3^2/M3^2] Log[Q^2/M3^2]-6 mQ3^6 mU3^10 Log[mU3^2/M3^2] Log[Q^2/M3^2]-2 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 (M3^2-mU3^2)^2 (-mQ3^4+mU3^4+2 M3^2 (mQ3^2-mU3^2)) PolyLog[2,M3^2/mQ3^2]+2 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 (M3^2-mU3^2)^2 (-mQ3^4+mU3^4+2 M3^2 (mQ3^2-mU3^2)) PolyLog[2,M3^2/mU3^2]))/(32 mQ3^2 (M3^2-mQ3^2)^2 mU3^2 (M3^2-mU3^2)^2 (mQ3^2-mU3^2)^4 \[Pi]^4)


(* ::Input:: *)
(*(*Shift DR to OS*)*)


(*sing[f_,x_,x0_,\[Delta]_]:={f[x0(1+\[Delta])](x-x0(1-\[Delta]))/(2x0 \[Delta])+f[x0(1-\[Delta])](1-1/(2x0 \[Delta])(x-x0(1-\[Delta]))),Abs[x/x0-1]<\[Delta]}*)
shiftDROS\[Alpha]t\[Alpha]S[mtilde_,mQ3_,mU3_,Xt_,M3_]:=Subscript[g, 3]^2 Subscript[g, t]^4 With[{\[Delta]=8.5 10^-2,\[Delta]2=1 10^-2},Piecewise[{{shiftDROS\[Alpha]t\[Alpha]Sdegenerate[mtilde,mQ3,Xt],Abs[mQ3/mU3-1]<\[Delta]2&&Abs[M3/mU3-1]<\[Delta]2&&Abs[M3/mQ3-1]<\[Delta]2},{Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mU3(1+\[Delta]),mU3,Xt ,M3]] (mQ3-mU3(1-\[Delta]))/(2mU3 \[Delta])+Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mU3(1-\[Delta]),mU3,Xt ,M3]](1-(mQ3-mU3(1-\[Delta]))/(2 mU3 \[Delta])),Abs[mQ3/mU3-1]< \[Delta]},
{Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mQ3,mU3,Xt ,mQ3(1+\[Delta])]] (M3-mQ3(1-\[Delta]))/(2mQ3 \[Delta])+Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mQ3,mU3,Xt ,mQ3(1-\[Delta])]](1-(M3-mQ3(1-\[Delta]))/(2mQ3 \[Delta])),Abs[mQ3/M3-1]<\[Delta]},
{Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mQ3,mU3,Xt ,mU3(1+\[Delta])]] (M3-mU3(1-\[Delta]))/(2mU3 \[Delta])+Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[1.mtilde,mQ3,mU3,Xt ,mU3(1-\[Delta])]](1-(M3-mU3(1-\[Delta]))/(2mU3 \[Delta])),Abs[mU3/M3-1]< \[Delta]}},Re[shiftDROS\[Alpha]t\[Alpha]Sgeneral[mtilde,1.mQ3,mU3,Xt ,M3]]]]


shiftDROS\[Alpha]t\[Alpha]Sgeneral[mtilde_,mQ3_,mU3_,QXt_,M3_]:=Re@ Block[{x1=(mQ3)^2/M3^2,x2=(mU3)^2/M3^2,xt=QXt/M3,xs=mtilde^2/M3^2},1/(64 \[Pi]^4) (-((2 ((-1+x1)^2 Log[1-x1]+x1 (3+x1-(-2+x1) Log[x1]+2 Log[xs/x1])))/x1^2)-(2 ((-1+x2)^2 Log[1-x2]+x2 (3+x2-(-2+x2) Log[x2]+2 Log[xs/x2])))/x2^2+1/(x1^2 x2^2) xt (1/(x1-x2)^3 x1^2 x2^2 (2 (x1-x2) xt^2+(2 x1^2+x2 (2 x2-xt^2)-x1 (4 x2+xt^2)) Log[x1/x2]) (-((4 xt^2 (x1 (-1+x2) Log[x1]-(-1+x1) x2 Log[x2]))/((-1+x1) (x1-x2) (-1+x2)))+1/(x1-x2) xt (-7 x1+x1/(-1+x1)+x1/(-1+x2)+7 x2+x2/(1-x1)+x2/(1-x2)-(4 (-1+x1)^2 Log[1-x1])/x1+((-x1+x2) Log[x1])/(-1+x1)^2-8 Log[1-x2]+(4 Log[1-x2])/x2+4 x2 Log[1-x2]-(x1 Log[x2])/(-1+x2)^2+(x2 Log[x2])/(-1+x2)^2+9 x1 Log[x1/xs]-x2 Log[x1/xs]+x1 Log[x2/xs]-9 x2 Log[x2/xs]+4 x1 Log[xs]-4 x2 Log[xs])-(4 ((-1+x1) x2 Log[1-x1]+x1 ((-1+x2) Log[1-x2]-2 x2 (2+Log[xs]))))/(x1 x2)+(xt ((-1+x1)^2 Log[1-x1]+x1 (3+x1-(-2+x1) Log[x1]+2 Log[xs/x1])))/x1^2+(xt ((-1+x2)^2 Log[1-x2]+x2 (3+x2-(-2+x2) Log[x2]+2 Log[xs/x2])))/x2^2)+xt (1/(x1-x2)^2 2 (-2 x1+2 x2+(x1+x2) Log[x1/x2]) ((-1+x1)^2 x2^2 Log[1-x1]-x1 ((-2+x1) x2^2 Log[x1]+x1 (-1+x2)^2 Log[1-x2]+x2 (3 x1-3 x2-x1 (-2+x2) Log[x2]-2 x2 Log[xs/x1]+2 x1 Log[xs/x2])))+x1^2 xt (1/(x1^2 (x1-x2)^3) 2 xt (-x1+x2+x1 Log[x1/x2]) ((-1+x1)^2 x2^2 Log[1-x1]-x1 ((-2+x1) x2^2 Log[x1]+x1 (-1+x2)^2 Log[1-x2]+x2 (3 x1-3 x2-x1 (-2+x2) Log[x2]-2 x2 Log[xs/x1]+2 x1 Log[xs/x2])))-1/((-1+x1/x2)^4 x2) (-2 x1+2 x2+(x1+x2) Log[x1/x2]) ((-1+x1/x2) (-((4 xt^2 (x1 (-1+x2) Log[x1]-(-1+x1) x2 Log[x2]))/((-1+x1) (x1-x2) (-1+x2)))+1/(x1-x2) xt (-7 x1+x1/(-1+x1)+x1/(-1+x2)+7 x2+x2/(1-x1)+x2/(1-x2)-(4 (-1+x1)^2 Log[1-x1])/x1+((-x1+x2) Log[x1])/(-1+x1)^2-8 Log[1-x2]+(4 Log[1-x2])/x2+4 x2 Log[1-x2]-(x1 Log[x2])/(-1+x2)^2+(x2 Log[x2])/(-1+x2)^2+9 x1 Log[x1/xs]-x2 Log[x1/xs]+x1 Log[x2/xs]-9 x2 Log[x2/xs]+4 x1 Log[xs]-4 x2 Log[xs])-(4 ((-1+x1) x2 Log[1-x1]+x1 ((-1+x2) Log[1-x2]-2 x2 (2+Log[xs]))))/(x1 x2)-(xt ((-1+x1)^2 Log[1-x1]+x1 (3+x1-(-2+x1) Log[x1]+2 Log[xs/x1])))/x1^2+(3 xt ((-1+x2)^2 Log[1-x2]+x2 (3+x2-(-2+x2) Log[x2]+2 Log[xs/x2])))/x2^2)+1/(x1 x2^3) 6 xt ((-1+x1)^2 x2^2 Log[1-x1]-x1 ((-2+x1) x2^2 Log[x1]+x1 (-1+x2)^2 Log[1-x2]+x2 (3 x1-3 x2-x1 (-2+x2) Log[x2]-2 x2 Log[xs/x1]+2 x1 Log[xs/x2]))))))))];
shiftDROS\[Alpha]t\[Alpha]Sdegenerate[mtilde_,M3_,Xt_]:=Re@ Block[{xt=Xt/M3,xs=mtilde^2/M3^2},((2+xt)^2 (-6+18 xt-9 xt^2+xt^3)+(-12+24 xt-6 xt^2-4 xt^3+xt^4) Log[xs])/(96 \[Pi]^4)];


(* ::Subsubsection::Closed:: *)
(*Two - Loop O((Subscript[\[Alpha], t]^2))*)


(* ::Text:: *)
(*The analytical expression for the two-loop O(Subscript[\[Alpha], t] Subscript[\[Alpha], s]) correction for degenerate scalars in the *)
(*\!\(\*OverscriptBox[\(DR\), \(_\)]\) scheme can be found in the definition of the function \[CapitalDelta]\[Lambda]2lalphat2[]. In the on-shell scheme one needs to add the shift contribution given in the function shiftDROS\[Alpha]t2[ ].*)


(* ::Text::Closed:: *)
(*Auxiliar*)


(* ::Input:: *)
(*\[CapitalDelta]\[Lambda]2lalphat2aux:=(3 ht^6 Sin[\[Beta]]^4)/(4\[Pi])^4 (1/2+6 \[Mu]h^2-(13 Cos[\[Beta]]^2)/2+60 K Cos[\[Beta]]^2+\[Pi]^2 Cos[\[Beta]]^2-8 f1[\[Mu]h]-2 \[Mu]h^2 f1[\[Mu]h]+3 \[Mu]h^2 f2[\[Mu]h]+4 f3[\[Mu]h]+Xth^6 (-(1/2)+Cos[\[Beta]]^2 (1/2-1/2 Log[mst^2/Q^2])+1/2 Log[mst^2/Q^2])-4 Log[mst^2/Q^2]-6 \[Mu]h^2 Log[mst^2/Q^2]+13 Cos[\[Beta]]^2 Log[mst^2/Q^2]+3 Log[mst^2/Q^2]^2-3 Cos[\[Beta]]^2 Log[mst^2/Q^2]^2+Xth^3 Yth (4 Cos[\[Beta]]^2+16 K Cos[\[Beta]]^2-2 Cos[\[Beta]]^2 Log[mst^2/Q^2])+Yth^2 (-3 Cos[\[Beta]]^2-16 K Cos[\[Beta]]^2+3 Cos[\[Beta]]^2 Log[mst^2/Q^2])+Xth Yth (-12 Cos[\[Beta]]^2-64 K Cos[\[Beta]]^2+12 Cos[\[Beta]]^2 Log[mst^2/Q^2])+Xth^2 (-7-6 \[Mu]h^2+15 Cos[\[Beta]]^2-24 K Cos[\[Beta]]^2+4 f1[\[Mu]h]-6 \[Mu]h^2 f1[\[Mu]h]-4 f2[\[Mu]h]-6 \[Mu]h^2 f2[\[Mu]h]+27 Log[mst^2/Q^2]+6 \[Mu]h^2 Log[mst^2/Q^2]-24 Cos[\[Beta]]^2 Log[mst^2/Q^2]+Yth^2 ((14 Cos[\[Beta]]^2)/3+24 K Cos[\[Beta]]^2-3 Cos[\[Beta]]^2 Log[mst^2/Q^2]))+Xth^4 (11/2+\[Mu]h^2-(25 Cos[\[Beta]]^2)/4-f1[\[Mu]h]/2+\[Mu]h^2 f1[\[Mu]h]+f2[\[Mu]h]/2+1/2 \[Mu]h^2 f2[\[Mu]h]-13/2 Log[mst^2/Q^2]-\[Mu]h^2 Log[mst^2/Q^2]+6 Cos[\[Beta]]^2 Log[mst^2/Q^2]+Yth^2 (-(19/12) Cos[\[Beta]]^2-8 K Cos[\[Beta]]^2+1/2 Cos[\[Beta]]^2 Log[mst^2/Q^2])));*)
(*\[CapitalDelta]\[Lambda]2lalphat2aux/.Log[1-\[Mu]h^2]->log[1-\[Mu]h^2]/.{\[Mu]h->\[Mu]/mst,Xth->Xt/mst,Yth->Xt/mst+(2\[Mu])/(mst Sin[2\[Beta]]),ht->Subscript[g, t]/Sin[\[Beta]]}/.{\[Beta]->ArcTan[tan\[Beta]]}*)


Module[{f1,f2,f3,\[Kappa]=1/(4\[Pi])^2,K=-0.1953256,\[Delta]=10^-5},
f1[\[Mu]_]:=Piecewise[{{-1,Abs[\[Mu]^2-1]<\[Delta]}},\[Mu]^2/(1-\[Mu]^2) Log[\[Mu]^2]];
f2[\[Mu]_]:=Piecewise[{{1/2,Abs[\[Mu]^2-1]<\[Delta]}},1/(1-\[Mu]^2) (1+\[Mu]^2/(1-\[Mu]^2) Log[\[Mu]^2])];
f3[\[Mu]_]:=Piecewise[{{-9/4,Abs[\[Mu]^2-1]<\[Delta]}},Re[(-1+2\[Mu]^2+2\[Mu]^4)/(1-\[Mu]^2)^2 (Log[\[Mu]^2]Log[1-\[Mu]^2]+PolyLog[2,\[Mu]^2]-\[Pi]^2/6-\[Mu]^2 Log[\[Mu]^2])]];
\[CapitalDelta]\[Lambda]2lalphat2[Q_,mst_,\[Mu]_,tan\[Beta]_,Xt_]:= \!\(
\*SubsuperscriptBox[\(g\), \(t\), \(6\)] 
\*FractionBox[\(1\), \(256\ 
\*SuperscriptBox[\(\[Pi]\), \(4\)]\ 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] 3\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\ \((
\*FractionBox[\(1\), \(2\)] - 
\*FractionBox[\(13\), \(2\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\)] + 
\*FractionBox[\(60\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[
SuperscriptBox[\(\[Pi]\), \(2\)], \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\), 
SuperscriptBox[\(mst\), \(2\)]] - 8\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]] - 
\*FractionBox[\(2\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 
\*FractionBox[\(3\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f2[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 4\ f3[
\*FractionBox[\(\[Mu]\), \(mst\)]] + 
\*FractionBox[\(
\*SuperscriptBox[\(Xt\), \(6\)]\ \((\(-
\*FractionBox[\(1\), \(2\)]\) + 
\*FractionBox[\(
\*FractionBox[\(1\), \(2\)] - 
\*FractionBox[\(1\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(1\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]])\)\), 
SuperscriptBox[\(mst\), \(6\)]] - 4\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]] + 
\*FractionBox[\(13\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 3\ 
\*SuperscriptBox[\(Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(2\)] - 
\*FractionBox[\(3\ 
\*SuperscriptBox[\(Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(2\)]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(1\), 
SuperscriptBox[\(mst\), \(3\)]] \(
\*SuperscriptBox[\(Xt\), \(3\)]\ \((
\*FractionBox[\(Xt\), \(mst\)] + 
\*FractionBox[\(2\ \[Mu]\ Csc[2\ ArcTan[tan\[Beta]]]\), \(mst\)])\)\ \((
\*FractionBox[\(4\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(16\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(2\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)])\)\) + 
\*SuperscriptBox[\((
\*FractionBox[\(Xt\), \(mst\)] + 
\*FractionBox[\(2\ \[Mu]\ Csc[2\ ArcTan[tan\[Beta]]]\), \(mst\)])\), \(2\)]\ \((\(-
\*FractionBox[\(3\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)]\) - 
\*FractionBox[\(16\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(3\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)])\) + 
\*FractionBox[\(1\), \(mst\)] \(Xt\ \((
\*FractionBox[\(Xt\), \(mst\)] + 
\*FractionBox[\(2\ \[Mu]\ Csc[2\ ArcTan[tan\[Beta]]]\), \(mst\)])\)\ \((\(-
\*FractionBox[\(12\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)]\) - 
\*FractionBox[\(64\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(12\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)])\)\) + 
\*FractionBox[\(1\), 
SuperscriptBox[\(mst\), \(2\)]] 
\*SuperscriptBox[\(Xt\), \(2\)]\ \((\(-7\) + 
\*FractionBox[\(15\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(24\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\), 
SuperscriptBox[\(mst\), \(2\)]] + 4\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]] - 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), 
SuperscriptBox[\(mst\), \(2\)]] - 4\ f2[
\*FractionBox[\(\[Mu]\), \(mst\)]] - 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f2[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 27\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]] - 
\*FractionBox[\(24\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(6\ 
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 
\*SuperscriptBox[\((
\*FractionBox[\(Xt\), \(mst\)] + 
\*FractionBox[\(2\ \[Mu]\ Csc[2\ ArcTan[tan\[Beta]]]\), \(mst\)])\), \(2\)]\ \((
\*FractionBox[\(14\), \(3\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\)] + 
\*FractionBox[\(24\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(3\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)])\))\) + 
\*FractionBox[\(1\), 
SuperscriptBox[\(mst\), \(4\)]] 
\*SuperscriptBox[\(Xt\), \(4\)]\ \((
\*FractionBox[\(11\), \(2\)] - 
\*FractionBox[\(25\), \(4\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\)] + 
\*FractionBox[
SuperscriptBox[\(\[Mu]\), \(2\)], 
SuperscriptBox[\(mst\), \(2\)]] - 
\*FractionBox[\(1\), \(2\)]\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]] + 
\*FractionBox[\(
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f1[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 
\*FractionBox[\(1\), \(2\)]\ f2[
\*FractionBox[\(\[Mu]\), \(mst\)]] + 
\*FractionBox[\(
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ f2[
\*FractionBox[\(\[Mu]\), \(mst\)]]\), \(2\ 
\*SuperscriptBox[\(mst\), \(2\)]\)] - 
\*FractionBox[\(13\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]] + 
\*FractionBox[\(6\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] - 
\*FractionBox[\(
\*SuperscriptBox[\(\[Mu]\), \(2\)]\ Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), 
SuperscriptBox[\(mst\), \(2\)]] + 
\*SuperscriptBox[\((
\*FractionBox[\(Xt\), \(mst\)] + 
\*FractionBox[\(2\ \[Mu]\ Csc[2\ ArcTan[tan\[Beta]]]\), \(mst\)])\), \(2\)]\ \((\(-
\*FractionBox[\(19\), \(12\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\)]\) - 
\*FractionBox[\(8\ K\), \(1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)]\)] + 
\*FractionBox[\(Log[
\*FractionBox[
SuperscriptBox[\(mst\), \(2\)], 
SuperscriptBox[\(Q\), \(2\)]]]\), \(2\ \((1 + 
\*SuperscriptBox[\(tan\[Beta]\), \(2\)])\)\)])\))\))\)\);
(*shift DRbar to OS*)
log[y_]:=Piecewise[{{0, Abs[y]<0.5 10^-2}},Log[Abs[y]]] ;(*defined to avoid numerical problems*)
shiftDROS\[Alpha]t2[Q_,mst_,\[Mu]_,tan\[Beta]_,Xt_]:=Subscript[g, t]^6 Re@Block[{\[Beta]=ArcTan[tan\[Beta]],xt=Xt/mst,yt=Xt/mst+(2 \[Mu])/(mst Sin[2ArcTan[tan\[Beta]]]),x\[Mu]=(\[Mu])^2/mst^2,xq=Q^2/mst^2},
Sin[\[Beta]]^-2 (1/(1024 \[Pi]^4) (-36-36 xt^2+6 xt^4+72 x\[Mu]-72 xt^2 x\[Mu]+12 xt^4 x\[Mu]-36 x\[Mu]^2+108 xt^2 x\[Mu]^2-18 xt^4 x\[Mu]^2) log[1-x\[Mu]]+1/(1024 \[Pi]^4) (108-54 xt^2+9 xt^4-108 x\[Mu]+180 xt^2 x\[Mu]-30 xt^4 x\[Mu]-6 xt^2 (-6+xt^2) x\[Mu] f2[Sqrt[x\[Mu]]]+3 (-24 (-1+x\[Mu])+12 xt^2 (3+2 x\[Mu])-2 xt^4 (3+2 x\[Mu])) Log[xq]+Cos[\[Beta]]^2 (36-48 (-6+Sqrt[3] \[Pi]) xt yt+8 (-6+Sqrt[3] \[Pi]) xt^3 yt+72 yt^2-12 Sqrt[3] \[Pi] yt^2+xt^4 (9-2 (-6+Sqrt[3] \[Pi]) yt^2)+6 xt^2 (-9+2 (-6+Sqrt[3] \[Pi]) yt^2)+6 (24 xt yt-4 xt^3 yt+6 (1+yt^2)-6 xt^2 (2+yt^2)+xt^4 (2+yt^2)) Log[xq])+36 x\[Mu]^2 Log[x\[Mu]]-108 xt^2 x\[Mu]^2 Log[x\[Mu]]+18 xt^4 x\[Mu]^2 Log[x\[Mu]]+6 xt^2 (30-10 xt^2+xt^4) (2+Log[xq]) Sin[\[Beta]]^2))]
]


(* ::Subsection::Closed:: *)
(*Global Functions*)


Options[\[Lambda]HSS]={hiOrd->{1,1,1},suppressedCorrections->False,scheme->"DRbar"};
\[Lambda]HSS[mtilde_?NumericQ,mQ1_?NumericQ,mQ2_?NumericQ,mQ3_?NumericQ,mU1_?NumericQ,mU2_?NumericQ,mU3_?NumericQ,mD1_?NumericQ,mD2_?NumericQ,mD3_?NumericQ,mE1_?NumericQ,mE2_?NumericQ,mE3_?NumericQ,mL1_?NumericQ,mL2_?NumericQ,mL3_?NumericQ,mA_?NumericQ,\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ,OptionsPattern[]]:=(\[Lambda]HSS1l[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt]+
If[OptionValue[hiOrd][[1]]==1,(\[CapitalDelta]\[Lambda]2lstrong[mtilde,mQ3,mU3,Xt,M3]+If[OptionValue[scheme]=="OS",shiftDROS\[Alpha]t\[Alpha]S[mtilde,mQ3,mU3,Xt,M3],0]),0]+If[OptionValue[hiOrd][[2]]==1,(\[CapitalDelta]\[Lambda]2lalphat2[mtilde,Sqrt[mQ3 mU3],\[Mu],tan\[Beta],Xt]+If[OptionValue[scheme]=="OS",shiftDROS\[Alpha]t2[mtilde,Sqrt[mQ3 mU3],\[Mu],tan\[Beta],Xt],0]),0]+
If[OptionValue[hiOrd][[3]]==1,(\[Lambda]2lbottom[mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]+\[Lambda]2ltau[mL3,mE3,M2,M1,\[Mu],tan\[Beta]]),0]+If[OptionValue[suppressedCorrections],\[Lambda]HSS1lsuppressed[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],0])


\[Lambda]Splitscalars[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[\[Lambda]Splitscalarsaux/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}]
\[Lambda]SMsplit[Qmsplit_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[\[Lambda]SMsplitaux/.{msplit->Qmsplit}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}]
gtSplitsplit[Qmsplit_,Q\[Mu]_?NumericQ,M1_,M2_,M3_]:=Simplify[gtSplitsplitaux/.{msplit->Qmsplit}/.{\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3}]


g1umtilde[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[g1umtildeaux/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}];
g2umtilde[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[g2umtildeaux/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}];
g1dmtilde[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[g1dmtildeaux/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}];
g2dmtilde[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Simplify[g2dmtildeaux/.{
\!\(\*OverscriptBox[\(m\), \(~\)]\)->mtilde}/.{Subscript[m, Subscript[Q, 1]]->mQ1,Subscript[m, Subscript[Q, 2]]->mQ2,Subscript[m, Subscript[Q, 3]]->mQ3,Subscript[m, Subscript[U, 1]]->mU1,Subscript[m, Subscript[U, 2]]->mU2,Subscript[m, Subscript[U, 3]]->mU3,Subscript[m, Subscript[D, 1]]->mD1,Subscript[m, Subscript[D, 2]]->mD2,Subscript[m, Subscript[D, 3]]->mD3,Subscript[m, Subscript[E, 1]]->mE1,Subscript[m, Subscript[E, 2]]->mE2,Subscript[m, Subscript[E, 3]]->mE3,Subscript[m, Subscript[L, 1]]->mL1,Subscript[m, Subscript[L, 2]]->mL2,Subscript[m, Subscript[L, 3]]->mL3,Subscript[m, A]->mA,\[Mu]->Q\[Mu],Subscript[M, 1]->M1,Subscript[M, 2]->M2,Subscript[M, 3]->M3,\[Beta]->ArcTan[tan\[Beta]],Subscript[X, t]->Xt}]


(* ::Title::Closed:: *)
(*Higgs Mass*)


(* ::Text:: *)
(*This is the actual package for the calcualtion of the Higgs mass in the MSSM. It depends on the other previously defined sub-packages: SM RGEs, Split RGEs and Thresholds.*)


(* ::Section::Closed:: *)
(*Matching at the electroweak scale (at the top mass)*)


Mhpole::usage="Mhpole[\[Lambda]atMT] computes the pole mass of the Higgs from the value of the quartic coupling \!\(\*
StyleBox[\"\[Lambda]atMT\",\nFontSlant->\"Italic\"]\) at the pole mass of the top in the \!\(\*OverscriptBox[\(MS\), \(_\)]\) scheme.";


(* ::Input:: *)
(* (*auxiliar*)*)
(*{(0.93684`/0.93690)^6 (-0.93690+0.94018),(-0.93690+0.94018)}*)


(*MW=80.385; MZ=91.1876;*)
Mh=125.09;
\[Alpha]3MZ=0.1185;
MT=173.34;MZ=91.1876;MW=80.385;
 GF=1.1663787 10^-5;vev=(Sqrt[2]GF)^(-1/2);
g3MT= 1.1666+0.00314 (\[Alpha]3MZ-0.1184)/0.0007-0.00046(MT-173.34);
g2MT= 0.64779;
gyMT= 0.35830;g1MT=Sqrt[5/3]gyMT;
gtMT3l=0.93690+0.00556(MT-173.34)-0.00042 (\[Alpha]3MZ-0.1184)/0.0007;(*NNNLO*)
gtMT2l=gtMT3l+0.00328;(*NNLO*);
gbMT=0.0156; 
g\[Tau]MT=0.0100; 
\[Lambda]MT=2(0.12604+0.00206(Mh-125.15)-0.00004(MT-173.34));


Options[SetSMparameters]={useMStopYukawa->False};
SetSMparameters[QMTorgt_,Q\[Alpha]3MZ_,opts:OptionsPattern[]]:=(If[!OptionValue[useMStopYukawa],
	g3MT=1.1666+0.00314 (Q\[Alpha]3MZ-0.1184)/0.0007-0.00046(QMTorgt-173.34);
	gtMT3l=0.93690+0.00556(QMTorgt-173.34)-0.00042 (Q\[Alpha]3MZ-0.1184)/0.0007;
	gtMT2l=gtMT3l+0.00328,(*if the use of the top Yukawa is chosed then*)
	gtMT3l=QMTorgt;
	gtMT2l=gtMT3l+0.00328;
	MT=173.34+1/0.00556 (gtMT3l-0.93690+0.00042 (Q\[Alpha]3MZ-0.1184)/0.0007);
	g3MT=1.1666+0.00314 (Q\[Alpha]3MZ-0.1184)/0.0007-0.00046(MT-173.34);];solSM3l=SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT3l,\[Lambda][0]==1/2 \[Lambda]MT,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,40,optsSMrun];
solSM2l=SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT2l,\[Lambda][0]==1/2 \[Lambda]MT,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,40,optsSMrun];)


QA0[m_,Q_]:=m^2 (1-Log[m^2/Q^2])
QB1[p_,m1_,m2_,Q_]:=1/(2p^2) (QA0[m2,Q]-QA0[m1,Q]+(p^2+m1^2-m2^2)QB0[p,m1,m2,Q])
QB0[p_,m1_,m2_,Q_]:=-Log[p^2/Q^2]-fB[xplus[p,m1,m2]]-fB[xminus[p,m1,m2]]
fB[x_]:=Log[1-x]-x Log[1-x^-1]-1
xplus[p_,m1_,m2_]:=(p^2-m2^2+m1^2+Sqrt[(p^2-m2^2+m1^2)^2-4p^2 m1^2])/(2p^2)
xminus[p_,m1_,m2_]:=(p^2-m2^2+m1^2-Sqrt[(p^2-m2^2+m1^2)^2-4p^2 m1^2])/(2p^2)
lambda1[vev_,mt_,mh_,MW_,MZ_,Q_]:=1/(16 \[Pi]^2 vev^4) Re[1/4 (mh^4+mh^2 (-6 mt^2+2 MW^2+MZ^2)-8 (2 MW^4+MZ^4))-(3 mh^2 MW^2 QA0[mh,Q])/(2 (mh^2-MW^2))+3 mh^2 QA0[mt,Q]+1/2 mh^2 (-11+(3 mh^2)/(mh^2-MW^2)-(3 MW^2)/(-MW^2+MZ^2)) QA0[MW,Q]+(mh^2 (7 MW^2-4 MZ^2) QA0[MZ,Q])/(2 (-MW^2+MZ^2))+9/4 mh^4 QB0[mh,mh,mh,Q]+3 mt^2 (mh^2-4 mt^2) QB0[mh,mt,mt,Q]+1/2 (mh^4-4 mh^2 MW^2+12 MW^4) QB0[mh,MW,MW,Q]+1/4 (mh^4-4 mh^2 MZ^2+12 MZ^4) QB0[mh,MZ,MZ,Q]]


\[Delta]\[Lambda]2lMT=Module[{\[Delta]\[Lambda]2QCD,\[Delta]\[Lambda]2EW},
\[Delta]\[Lambda]2QCD=g3MT^2/(4\[Pi])^4 (-23.88+0.12(Mh-125)-0.64 (MT-173));
\[Delta]\[Lambda]2EW=1/(4\[Pi])^4 (-9.45-0.12 (Mh-125)-0.21(MT-173));
-2\[Delta]\[Lambda]2QCD-2 \[Delta]\[Lambda]2EW];


Mhpole[\[Lambda]mt_]:=Sqrt[vev^2 (\[Lambda]mt-  2lambda1[vev,MT,Sqrt[\[Lambda]mt vev^2],MW,MZ,MT]+ \[Delta]\[Lambda]2lMT)]


(* ::Section::Closed:: *)
(*Pole mass of the Higgs in the MSSM*)


(* ::Subsection::Closed:: *)
(*Interpolated Solution of the RGEs*)


(* ::Subsubsection::Closed:: *)
(*Generating the Table*)


(* ::Input:: *)
(*Flatten[Table[{{\[Lambda]high,thigh},2\[Lambda][0]/.SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT3l,\[Lambda][thigh]==1/2 \[Lambda]high,Subscript[g, \[Tau]][0]==g\[Tau]MT,Subscript[g, b][0]==gbMT},0,thigh,optsSMrun]},{\[Lambda]high,0,0.41,20 0.01},{thigh,0.4,40,10}],1](*test before running the full table below*)*)


(* ::Input:: *)
(*\[Delta]gtMT=0.00556( 2.1 0.76);\[Delta]g3MT=1.1 0.00314 0.0006/0.0007+0.00046(2 0.76);*)
(*tablethigh=Join[Table[i,{i,0.4,2,0.2}],Table[i,{i,2.2,6,0.4}],Table[i,{i,6.2,40,0.6}]]*)
(*table\[Lambda]high=Join[Table[i,{i,-0.03,0.27,0.03}],Table[i,{i,0.3,0.4,0.06}]]*)


(* ::Input:: *)
(*Clear[list];list={};*)
(*Do[list=Join[list,{{{\[Lambda]high,thigh,gtMTvar,g3MTvar},2\[Lambda][0]/.SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMTvar,\[Lambda][thigh]==1/2 \[Lambda]high,Subscript[g, \[Tau]][0]==g\[Tau]MT,Subscript[g, b][0]==gbMT},0,thigh,optsSMrun]}}],{\[Lambda]high,(*-0.03,0.41,0.03*)table\[Lambda]high},{thigh,(*0.4,39,0.3*)tablethigh},{gtMTvar,{gtMT3l,gtMT3l+\[Delta]gtMT,gtMT3l-\[Delta]gtMT}},{g3MTvar,{g3MT,g3MT+\[Delta]g3MT,g3MT-\[Delta]g3MT}}];*)


(* ::Subsubsection::Closed:: *)
(*Saved Table*)


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(* ::Subsubsection::Closed:: *)
(*Interpolation*)


(* ::Text:: *)
(*The table in the subsection above contains the solution of the renormalization group equations of the SM (allowing for different boundary conditions for the quartic coupling). The solution is interpolated to avoid slow numerical integrations.*)


\[Lambda]atMTint=Quiet@Interpolation[tableint];


(* ::Subsection::Closed:: *)
(*High - Scale*)


positiveQ[x_]:=If[Im[x]==0,x>0,False]
Options[MhpoleHSS]={hiOrd->{1,1,1,1},scheme->"DRbar"};
MhpoleHSS[mtilde_?positiveQ,mQ1_?positiveQ,mQ2_?positiveQ,mQ3_?positiveQ,mU1_?positiveQ,mU2_?positiveQ,mU3_?positiveQ,mD1_?positiveQ,mD2_?positiveQ,mD3_?positiveQ,mE1_?positiveQ,mE2_?positiveQ,mE3_?positiveQ,mL1_?positiveQ,mL2_?positiveQ,mL3_?positiveQ,mA_?positiveQ,Q\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ,opts:OptionsPattern[]]:=Block[{tmax=Rationalize[Log[mtilde/MT],10^-5],\[Lambda]mtilde,\[Lambda]MT},
\[Lambda]mtilde=\[Lambda]HSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,opts]/.{Subscript[g, 1]->Subscript[g, 1][tmax],Subscript[g, 2]->Subscript[g, 2][tmax],Subscript[g, 3]->Subscript[g, 3][tmax],Subscript[g, t]->Subscript[g, t][tmax],\[Lambda]->\[Lambda][tmax],Subscript[g, \[Tau]]->Subscript[g, \[Tau]][tmax],Subscript[g, b]->Subscript[g, b][tmax]};
\[Lambda]MT=(2\[Lambda][0]/.SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==If[OptionValue[hiOrd][[4]]==0,gtMT2l,gtMT3l],\[Lambda][tmax]==1/2 \[Lambda]mtilde,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,tmax,optsSMrun]);
Mhpole[\[Lambda]MT]
]


Options[MhpoleHSSfast]={hiOrd->{1,1,1,1},scheme->"DRbar"};
solSM2l=SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT2l,\[Lambda][0]==1/2 \[Lambda]MT,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,40,optsSMrun];
solSM3l=SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT3l,\[Lambda][0]==1/2 \[Lambda]MT,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,40,optsSMrun];
solutionSMRGEs=solSM3l/.{g1->"g1",g2->"g2",g3->"g3",gt->"gt",\[Lambda]->"\[Lambda]",g\[Tau]->"g\[Tau]",gb->"gb"};
(*This solution is an external variable for convenience.*)
MhpoleHSSfast[mtilde_?positiveQ,mQ1_?positiveQ,mQ2_?positiveQ,mQ3_?positiveQ,mU1_?positiveQ,mU2_?positiveQ,mU3_?positiveQ,mD1_?positiveQ,mD2_?positiveQ,mD3_?positiveQ,mE1_?positiveQ,mE2_?positiveQ,mE3_?positiveQ,mL1_?positiveQ,mL2_?positiveQ,mL3_?positiveQ,mA_?positiveQ,Q\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ,opts:OptionsPattern[]]:=Block[{\[Lambda]mtilde,evaluate,tmtilde,\[Lambda]\[Lambda]},(tmtilde=Log[mtilde/MT];
evaluate={\[Lambda]\[Lambda]->\[Lambda][tmtilde],Subscript[g, t]->gt[tmtilde],Subscript[g, 3]->g3[tmtilde],Subscript[g, 2]->g2[tmtilde],Subscript[g, 1]->g1[tmtilde],Subscript[g, b]->gb[tmtilde],Subscript[g, \[Tau]]->g\[Tau][tmtilde]}/.If[OptionValue[hiOrd][[4]]==0,solSM2l,solSM3l];
\[Lambda]mtilde=(\[Lambda]HSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,opts]/.evaluate/.{\[Lambda]\[Lambda]->\[Lambda]});
Mhpole[Quiet@\[Lambda]atMTint[\[Lambda]mtilde,tmtilde,If[OptionValue[hiOrd][[4]]==0,gtMT2l,gtMT3l],g3MT]])]


(* ::Subsection::Closed:: *)
(*Split*)


Module[{g1SM,g2SM,g3SM,gtSM,evaluateintmtilde,evaluateintmsplit,\[Lambda]Splitmtilde,gtSplitmsplit,g1utmtilde,g2utmtilde,g1dtmtilde,g2dtmtilde,\[Lambda]Splitsplit,tmtilde,tmsplit,solsplit,rules,\[Lambda]SMtmsplit,\[Lambda]SMMT},
rules={Subscript[g, 1]->g1,Subscript[g, 2]->g2,Subscript[g, 3]->g3,Subscript[g, t]->gt,Subscript[g, \[Tau]]->g\[Tau],Subscript[g, b]->gb,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u]->gtildeu,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u]->gtilde2u,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d]->gtilded,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d]->gtilde2d};
g1SM[Qtup_]:=g1[Qtup]/.solSM3l;
g2SM[Qtup_]:=g2[Qtup]/.solSM3l;
g3SM[Qtup_]:=g3[Qtup]/.solSM3l;
gtSM[Qtup_]:=gt[Qtup]/.solSM3l;
evaluateintmtilde=(#->#[tmtilde]&/@{\[Lambda],Subscript[g, t],Subscript[g, 3],Subscript[g, 2],Subscript[g, 1],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1d],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2d],Subscript[g, b],Subscript[g, \[Tau]]});
evaluateintmsplit=(#->#[tmsplit]&/@{\[Lambda],Subscript[g, t],Subscript[g, 3],Subscript[g, 2],Subscript[g, 1],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1d],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2d],Subscript[g, b],Subscript[g, \[Tau]]});
MhpoleSplit[mtilde_?positiveQ,msplit_?positiveQ,mQ1_?positiveQ,mQ2_?positiveQ,mQ3_?positiveQ,mU1_?positiveQ,mU2_?positiveQ,mU3_?positiveQ,mD1_?positiveQ,mD2_?positiveQ,mD3_?positiveQ,mE1_?positiveQ,mE2_?positiveQ,mE3_?positiveQ,mL1_?positiveQ,mL2_?positiveQ,mL3_?positiveQ,mA_?positiveQ,Q\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ]:=(
(*Avoids instability of the solution for small running, when tmtilde and tmsplit are close.*)
tmtilde=Rationalize[Log[mtilde/MT],10^-5];
tmsplit=Rationalize[Log[msplit/MT],10^-5];
\[Lambda]Splitmtilde=\[Lambda]Splitscalars[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmtilde;
gtSplitmsplit=(gtSplitsplit[msplit,Q\[Mu],M1,M2,M3]/.evaluateintmsplit/.{Subscript[g, t]->gtSM});
g1utmtilde=g1umtilde[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmtilde;
g2utmtilde=g2umtilde[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmtilde;
g1dtmtilde=g1dmtilde[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmtilde;
g2dtmtilde=g2dmtilde[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmtilde;
solsplit=Splitrun[{\[Lambda],Subscript[g, 3],Subscript[g, 2],Subscript[g, 1],Subscript[g, t],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 u],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1 d],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2 d],Subscript[g, b],Subscript[g, \[Tau]]},{\[Lambda][tmtilde]==\[Lambda]Splitmtilde,Subscript[g, t][tmsplit]==gtSplitmsplit,Subscript[g, 3][tmsplit]==g3SM[tmsplit],Subscript[g, 2][tmsplit]==g2SM[tmsplit],Subscript[g, 1][tmsplit]==g1SM[tmsplit],Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1u][tmtilde]==g1utmtilde,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2u][tmtilde]==g2utmtilde,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 1d][tmtilde]==g1dtmtilde,Subscript[
\!\(\*OverscriptBox[\(g\), \(~\)]\), 2d][tmtilde]==g2dtmtilde,Subscript[g, b][tmsplit]==gbMT,Subscript[g, \[Tau]][tmsplit]==g\[Tau]MT},tmsplit,tmtilde,optsSplitrun];
\[Lambda]SMtmsplit=(\[Lambda]SMsplit[msplit,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]/.evaluateintmsplit/.rules)/.solsplit;
\[Lambda]SMMT=2\[Lambda][0]/.SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT3l,\[Lambda][tmsplit]==1/2 \[Lambda]SMtmsplit,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,tmsplit,optsSMrun];Mhpole[\[Lambda]SMMT]
)]


(* ::Subsection::Closed:: *)
(*MHiggs Function*)


(* ::Subsubsection::Closed:: *)
(*Tests*)


(*It returns a list to be used as the argument for function which computes the Higgs mass.*)
getList[x_]:=Block[{list},Switch[Length[x],2,With[{tan\[Beta]=x[[1]],m0=x[[2]]},list={tan\[Beta],m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
3,With[{tan\[Beta]=x[[1]],m0=x[[2]],At=x[[3]]},list={tan\[Beta],m0,m0,m0,m0,At,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
4,With[{tan\[Beta]=x[[1]],m0=x[[2]],At=x[[3]],m12=x[[4]]},list={tan\[Beta],m12,m12,m12,m12,At,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
5,With[{tan\[Beta]=x[[1]],m0=x[[2]],At=x[[3]],m12=x[[4]],\[Mu]=x[[5]]},list={tan\[Beta],m12,m12,m12,\[Mu],At,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
6,With[{tan\[Beta]=x[[1]],mQ3=x[[2]],mU3=x[[3]],At=x[[4]],m12=x[[5]],\[Mu]=x[[6]],m0=Sqrt[x[[2]]x[[3]]]},list={tan\[Beta],m12,m12,m12,\[Mu],At,mQ3,mU3,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
8,With[{tan\[Beta]=x[[1]],mQ3=x[[2]],mU3=x[[3]],At=x[[4]],M1=x[[5]],M2=x[[6]],M3=x[[7]],\[Mu]=x[[8]],m0=Sqrt[x[[2]]x[[3]]]},list={tan\[Beta],M1,M2,M3,\[Mu],At,mQ3,mU3,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0,m0}],
22,list=x,
_,list=Table[0,{i,22}]
];
list
]


gtMSSM[Q_,tan\[Beta]_]:=((gt[Log[Q/MT]]/.solSM3l)/Sin[ArcTan[tan\[Beta]]])
gbMSSM[Q_,mQ3_,mU3_,mD3_,M3_,\[Mu]_,tan\[Beta]_,Xt_]:=Block[{gbDRbar,tRG,evaluate},
tRG=Log[Q/MT];
evaluate={Subscript[g, t]->gt[tRG],Subscript[g, 3]->g3[tRG],Subscript[g, b]->gb[tRG]}/.solSM3l;
gbDRbar=gbDR[mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]/.evaluate
]
testgbDR[Q_,mQ3_,mU3_,mD3_,M3_,\[Mu]_,tan\[Beta]_,Xt_]:=With[{gbDRbar=gbMSSM[Q,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]},
Which[4<Abs@gbDRbar<4\[Pi],Message[MHiggs::bottomYukawa],
Abs@gbDRbar>=4\[Pi],Message[MHiggs::bottomYukawa];True]]


gtauMSSM[Q_,mL3_,mE3_,M2_,M1_,\[Mu]_,tan\[Beta]_]:=Block[{gtauDRbar,tRG,evaluate},
tRG=Log[Q/MT];
evaluate={Subscript[g, 1]->g1[tRG],Subscript[g, 2]->g2[tRG],Subscript[g, \[Tau]]->g\[Tau][tRG]}/.solSM3l;
gtauDRbar=gtauDR[mL3,mE3,M2,M1,\[Mu],tan\[Beta]]/.evaluate
]
testgtauDR[Q_,mL3_,mE3_,M2_,M1_,\[Mu]_,tan\[Beta]_]:=
With[{gtauDRbar=gtauMSSM[Q,mL3,mE3,M2,M1,\[Mu],tan\[Beta]]},Which[4<Abs@gtauDRbar<4\[Pi],Message[MHiggs::tauYukawa],
Abs@gtauDRbar>=4\[Pi],Message[MHiggs::tauYukawa];True]]


(* ::Subsubsection::Closed:: *)
(*Function*)


numericListQ[list_]:=(If[Not@ListQ[list],Return[False]];And@@Table[If[NumericQ[element],True,False],{element,list}])
(*ensure a numeric list as a variable for MHiggs*)
cond[m_]:=(NumericQ[m]&&Im[m]==0&&Abs[m]>175);(*condition for the soft masses*)
Options[MHiggs]={hiOrd->{1,1,1,1},numerical->False,split->False,Rscale->0,RscaleSplit->0,scheme->"DRbar"};
MHiggs[shortList_?numericListQ,opts:OptionsPattern[]]:=Block[{tan\[Beta],M1,M2,M3,\[Mu],At,mQ3,mU3,mD3,mQ2,mU2,mD2,mQ1,mU1,mD1,mL3,mE3,mL2,mE2,mL1,mE1,mA,Xt,mtilde,msplit,mh},
{tan\[Beta],M1,M2,M3,\[Mu],At,mQ3,mU3,mD3,mQ2,mU2,mD2,mQ1,mU1,mD1,mL3,mE3,mL2,mE2,mL1,mE1,mA}=getList[shortList];
Xt=At-\[Mu] /tan\[Beta];msplit=If[OptionValue[RscaleSplit]<200,Max[\[Mu],M2],OptionValue[RscaleSplit]];mtilde=If[OptionValue[Rscale]<200,Sqrt[mQ3 mU3],OptionValue[Rscale]];
If[NumericQ[tan\[Beta]]&&tan\[Beta]>=1&&cond[M1]&&cond[M2]&&cond[M3]&&cond[\[Mu]]&&Im[At]==0&&NumericQ[At]&&cond[mQ3]&&cond[mU3]&&cond[mD3]&&cond[mQ2]&&cond[mU2]&&cond[mD2]&&cond[mQ1]&&cond[mU1]&&cond[mD1]&&cond[mL3]&&cond[mE3]&&cond[mL2]&&cond[mE2]&&cond[mL1]&&cond[mE1]&&cond[mA],1,Message[MHiggs::variables];Return[0]];
If[Not[1/10<=mtilde/Sqrt[mQ3 mU3]<=10]||0<OptionValue[Rscale]<200,Message[MHiggs::warning]];
If[testgbDR[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt],Return[0]];
If[testgtauDR[mtilde,mL3,mE3,M2,M1,\[Mu],tan\[Beta]],Return[0]];
Which[
Not[OptionValue@split]&& Not[OptionValue@numerical],
mh=MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{hiOrd,scheme}]],
Not[OptionValue@split]&&OptionValue@numerical,
mh=MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{hiOrd,scheme}]],
OptionValue@split&&(msplit<mtilde),
mh=MhpoleSplit[mtilde,msplit,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],
OptionValue@split&&(msplit>=mtilde),
(Message[MHiggs::warningsplit];
mh=MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{hiOrd}]])
];
If[Im[mh]==0,mh,Message[MHiggs::negative](*;Print[mh]*);0]
]


(* ::Section::Closed:: *)
(*Theoretical uncertainties*)


(* ::Subsection::Closed:: *)
(*EFT: v^2/*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*StyleBox["SUSY",*)
(*FontSize->12], \(2\)]\)-suppressed corrections*)


MhpoleHSSmom[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Block[{\[Lambda]mtilde,evaluate,tmtilde,\[Lambda]\[Lambda]},(tmtilde=Log[mtilde/MT];
evaluate={\[Lambda]\[Lambda]->\[Lambda][tmtilde],Subscript[g, t]->gt[tmtilde],Subscript[g, 3]->g3[tmtilde],Subscript[g, 2]->g2[tmtilde],Subscript[g, 1]->g1[tmtilde],Subscript[g, b]->gb[tmtilde],Subscript[g, \[Tau]]->g\[Tau][tmtilde]}/.solSM3l/.{\[Lambda]\[Lambda]->\[Lambda]};
\[Lambda]mtilde=(\[Lambda]HSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0},suppressedCorrections->True])/.evaluate);
\[Lambda]MT=(2\[Lambda][0]/.SMrun[{Subscript[g, 1],Subscript[g, 2],Subscript[g, 3],Subscript[g, t],\[Lambda],Subscript[g, \[Tau]],Subscript[g, b]},{Subscript[g, 1][0]==g1MT,Subscript[g, 2][0]==g2MT,Subscript[g, 3][0]==g3MT,Subscript[g, t][0]==gtMT3l,\[Lambda][tmax]==1/2 \[Lambda]mtilde,Subscript[g, b][0]==gbMT,Subscript[g, \[Tau]][0]==g\[Tau]MT},0,tmax,optsSMrun]);
Mhpole[\[Lambda]MT]
]


MhpoleHSSmomfast[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=Block[{\[Lambda]mtilde,evaluate,tmtilde,\[Lambda]\[Lambda]},(tmtilde=Log[mtilde/MT];
evaluate={\[Lambda]\[Lambda]->\[Lambda][tmtilde],Subscript[g, t]->gt[tmtilde],Subscript[g, 3]->g3[tmtilde],Subscript[g, 2]->g2[tmtilde],Subscript[g, 1]->g1[tmtilde],Subscript[g, b]->gb[tmtilde],Subscript[g, \[Tau]]->g\[Tau][tmtilde]}/.solSM3l/.{\[Lambda]\[Lambda]->\[Lambda]};
\[Lambda]mtilde=(\[Lambda]HSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0},suppressedCorrections->True])/.evaluate);
Mhpole[Quiet@\[Lambda]atMTint[\[Lambda]mtilde,tmtilde,gtMT3l,g3MT]]]


\[CapitalDelta]MhpoleHSSmom[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=Abs[MhpoleHSSmom[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]-MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0,1}]]


\[CapitalDelta]MhpoleHSSmomfast[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,Q\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=Abs[MhpoleHSSmomfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt]-MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,Q\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0,1}]]


(* ::Subsection::Closed:: *)
(*SM higher order corrections*)


Options[\[CapitalDelta]MhpoleHSSSMfast]={scheme->"DRbar"};
\[CapitalDelta]MhpoleHSSSM[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=Abs[MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{1,0,0,1},opts]-MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{1,0,0,0},opts]]+0.15


Options[\[CapitalDelta]MhpoleHSSSMfast]={scheme->"DRbar"};
\[CapitalDelta]MhpoleHSSSMfast[mtilde_,mQ1_?NumericQ,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=Abs[MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{1,0,0,1},opts]-MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{1,0,0,0},opts]]+0.15


(* ::Subsection::Closed:: *)
(*SUSY: Variation of the renormalization scale*)


(* ::Subsubsection::Closed:: *)
(*Manipulation*)


(* ::Input:: *)
(*\[Beta]\[Beta][Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]]:=1/(4\[Pi])^2 Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t](6Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]^2-16/3 Subscript[g, 3]^2-3Subscript[g, 2]^2-13/15 Subscript[g, 1]^2)*)
(*\[Beta]\[Beta][\[Mu]]:=\[Mu]/(4\[Pi])^2 (3Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]^2+3Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), b]^2+Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), \[Tau]]^2- 3Subscript[g, 2]^2- 3/5 Subscript[g, 1]^2)*)
(*\[Beta]\[Beta][Subscript[a, t]]:=1/(4\[Pi])^2 Subscript[a, t](18Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]^2-16/3 Subscript[g, 3]^2-3Subscript[g, 2]^2-13/15 Subscript[g, 1]^2)+1/(4\[Pi])^2 Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t](32/3 Subscript[g, 3]^2 Subscript[M, 3]+6Subscript[g, 2]^2 Subscript[M, 2]+26/15 Subscript[g, 1]^2 Subscript[M, 1])*)
(*Subscript[XX, t]:=2 *)
(*\!\(\*SubsuperscriptBox[*)
(*OverscriptBox[\(g\), \(^\)], \(t\), \(2\)]\) (\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(u\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(u\), \(3\)], \(2\)]\))+2 Subscript[a, t]^2;*)
(*Subscript[XX, b]:=2 *)
(*\!\(\*SubsuperscriptBox[*)
(*OverscriptBox[\(g\), \(^\)], \(b\), \(2\)]\) (\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(u\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(u\), \(3\)], \(2\)]\))+2 Subscript[a, b]^2;*)
(*Subscript[XX, \[Tau]]:=2 *)
(*\!\(\*SubsuperscriptBox[*)
(*OverscriptBox[\(g\), \(^\)], \(\[Tau]\), \(2\)]\) (\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(u\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(L\), \(3\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(e\), \(3\)], \(2\)]\))+2 Subscript[a, \[Tau]]^2;*)
(*Subscript[a, t]:=Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t] Subscript[A, t];Subscript[a, b]:=Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), b] Subscript[A, b];Subscript[a, \[Tau]]:=Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), \[Tau]] Subscript[A, \[Tau]];*)
(*S := \!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(u\)], \(2\)] - *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(d\)], \(2\)] + \( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(3\)]\(( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(i\)], \(2\)] - *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(L\), \(i\)], \(2\)] - 2\ *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(u\), \(i\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(d\), \(i\)], \(2\)] + *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(e\), \(i\)], \(2\)])\)\)\);*)
(*\[Beta]\[Beta][*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(u\)], \(2\)]\)]:=1/(16\[Pi]^2) (3 Subscript[XX, t]-6 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(2\), \(2\)]\)-6/5 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(1\), \(2\)]\)+ (3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) S)/5);\[Beta]\[Beta][*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(H\), \(d\)], \(2\)]\)]:=1/(16\[Pi]^2) (3 Subscript[XX, b]+Subscript[XX, \[Tau]]-6 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(2\), \(2\)]\)-6/5 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(1\), \(2\)]\)-(3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) S)/5);*)
(*\[Beta]\[Beta][*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)]\)]:=1/(16\[Pi]^2) (Subscript[XX, t]-32/3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-6 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(2\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(2\), \(2\)]\)-2/15 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(1\), \(2\)]\)+(\!\( *)
(*\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\ S\))/5);\[Beta]\[Beta][*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(u\), \(3\)], \(2\)]\)]:=1/(16\[Pi]^2) (2Subscript[XX, t]-32/3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-32/15 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(1\), \(2\)]\)-(4 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) S)/5);*)
(*\[Beta]\[Beta][*)
(*\!\(\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(d\), \(3\)], \(2\)]\)]:=1/(16\[Pi]^2) (2Subscript[XX, b]-32/3 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(3\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(3\), \(2\)]\)-8/15 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) *)
(*\!\(\*SubsuperscriptBox[\(M\), \(1\), \(2\)]\)+2/5 *)
(*\!\(\*SubsuperscriptBox[\(g\), \(1\), \(2\)]\) S);*)
(*\[Beta]\[Beta][Subscript[X, t]]:=\[Beta]\[Beta][Subscript[A, t]]-\[Beta]\[Beta][\[Mu]]/Tan[\[Beta]]+\[Mu]/(2Tan[\[Beta]]^3) \[Beta]\[Beta][tan\[Beta]^2]*)
(*\[Beta]\[Beta][Subscript[A, t]]:=Simplify[1/Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t] (\[Beta]\[Beta][Subscript[a, t]]-\[Beta]\[Beta][Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]]Subscript[A, t])]*)
(*Subscript[\[Gamma], 2]:=1/(64\[Pi]^2) (9Subscript[g, 2]^2+3Subscript[g, 1]^2-12Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]^2-6Subscript[g, 2]^2-2Subscript[g, 1]^2)*)
(*Subscript[\[Gamma], 1]:=1/(64\[Pi]^2) (9Subscript[g, 2]^2+3Subscript[g, 1]^2-6Subscript[g, 2]^2-2Subscript[g, 1]^2)*)
(*\[Beta]\[Beta][tan\[Beta]^2]:=2Tan[\[Beta]]^2 (Subscript[\[Gamma], 2]-Subscript[\[Gamma], 1])*)
(*replacements1:={d->D,e->E,u->U,Subscript[m, Subscript[H, u]]^2->mA^2 Cos[\[Beta]]^2-\[Mu]^2,Subscript[m, Subscript[H, d]]^2->mA^2 Sin[\[Beta]]^2-\[Mu]^2,Subscript[XX, \[Tau]]->0,Subscript[A, t]->Xt+\[Mu] Cot[\[Beta]],Subscript[A, b]->0,Subscript[A, \[Tau]]->0};*)
(*replacements2:={Subscript[m, Subscript[x_, y_]]^2:>Symbol["m"<>ToString[x]<>ToString[y]]^2,Subscript[M, x_]:>Symbol["M"<>ToString[x]],Subscript[X, t]->Xt,\[Beta]->ArcTan[tan\[Beta]],Subscript[g, 1]->g1SM[Log[mtilde/MT]],Subscript[g, 2]->g2SM[Log[mtilde/MT]],Subscript[g, 3]->g3SM[Log[mtilde/MT]],*)
(*Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), t]->gtMSSM[mtilde,tan\[Beta]],Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), b]->gbMSSM[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt],Subscript[*)
(*\!\(\*OverscriptBox[\(g\), \(^\)]\), \[Tau]]->gtauMSSM[mtilde,mL3,mE3,M2,M1,\[Mu],tan\[Beta]]};*)


(* ::Input:: *)
(*{mQ3^2+\[Beta]\[Beta][Subscript[m, Subscript[Q, 3]]^2]Log[n],mU3^2+\[Beta]\[Beta][Subscript[m, Subscript[u, 3]]^2]Log[n],mD3^2+\[Beta]\[Beta][Subscript[m, Subscript[d, 3]]^2]Log[n],\[Mu]+\[Beta]\[Beta][\[Mu]]Log[n],Subscript[X, t]+\[Beta]\[Beta][Subscript[X, t]]Log[n]}/.replacements1/.replacements2*)


(* ::Input:: *)
(*(*OS scheme*)*)
(*\[Beta]\[Beta][XtOS]:=1/(4\[Pi])^2 Xt(8Subscript[g, 3]^2-3/2 Subscript[g, t]^2)*)
(*Xt+\[Beta]\[Beta][XtOS]Log[n]/.{Subscript[g, 3]->g3SM[Log[mtilde/MT]],Subscript[g, t]->gtSM[Log[mtilde/MT]]}*)


(* ::Subsubsection::Closed:: *)
(*Variation of the spectrum*)


(* ::Text:: *)
(*At the moment(\!\( *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(Q\), \(3\)], \(2\)], *)
(*\*SubsuperscriptBox[\(m\), *)
(*SubscriptBox[\(U\), \(3\)], \(2\)], *)
(*\*SuperscriptBox[*)
(*SubscriptBox[\(m\), *)
(*SubscriptBox[\(D\), \(3\)]], \(2\)], \[Mu], *)
(*\*SubscriptBox[\(X\), \(t\)]\))are varied.*)


Module[{g1SM,g2SM,g3SM,gtSM},
g1SM[Qtup_]:=g1[Qtup]/.solSM3l;
g2SM[Qtup_]:=g2[Qtup]/.solSM3l;
g3SM[Qtup_]:=g3[Qtup]/.solSM3l;
gtSM[Qtup_]:=gt[Qtup]/.solSM3l;
spectrum[n_,mtilde_,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:={mQ3^2+1/(16 \[Pi]^2) (-(2/15) M1^2 g1SM[Log[mtilde/MT]]^2+1/5 (mD1^2+mD2^2+mD3^2+mE1^2+mE2^2+mE3^2-mL1^2-mL2^2-mL3^2+mQ1^2+mQ2^2+mQ3^2-2 mU1^2-2 mU2^2-2 mU3^2+mA^2/(1+tan\[Beta]^2)-(mA^2 tan\[Beta]^2)/(1+tan\[Beta]^2)) g1SM[Log[mtilde/MT]]^2-6 M2^2 g2SM[Log[mtilde/MT]]^2-32/3 M3^2 g3SM[Log[mtilde/MT]]^2+2 (Xt+\[Mu]/tan\[Beta])^2 gtMSSM[mtilde,tan\[Beta]]^2+2 (mQ3^2+mU3^2+mA^2/(1+tan\[Beta]^2)-\[Mu]^2) gtMSSM[mtilde,tan\[Beta]]^2) Log[n],mU3^2+1/(16 \[Pi]^2) (-(32/15) M1^2 g1SM[Log[mtilde/MT]]^2-4/5 (mD1^2+mD2^2+mD3^2+mE1^2+mE2^2+mE3^2-mL1^2-mL2^2-mL3^2+mQ1^2+mQ2^2+mQ3^2-2 mU1^2-2 mU2^2-2 mU3^2+mA^2/(1+tan\[Beta]^2)-(mA^2 tan\[Beta]^2)/(1+tan\[Beta]^2)) g1SM[Log[mtilde/MT]]^2-32/3 M3^2 g3SM[Log[mtilde/MT]]^2+2 (2 (Xt+\[Mu]/tan\[Beta])^2 gtMSSM[mtilde,tan\[Beta]]^2+2 (mQ3^2+mU3^2+mA^2/(1+tan\[Beta]^2)-\[Mu]^2) gtMSSM[mtilde,tan\[Beta]]^2)) Log[n],mD3^2+1/(16 \[Pi]^2) (-(8/15) M1^2 g1SM[Log[mtilde/MT]]^2+2/5 (mD1^2+mD2^2+mD3^2+mE1^2+mE2^2+mE3^2-mL1^2-mL2^2-mL3^2+mQ1^2+mQ2^2+mQ3^2-2 mU1^2-2 mU2^2-2 mU3^2+mA^2/(1+tan\[Beta]^2)-(mA^2 tan\[Beta]^2)/(1+tan\[Beta]^2)) g1SM[Log[mtilde/MT]]^2-32/3 M3^2 g3SM[Log[mtilde/MT]]^2+4 (mQ3^2+mU3^2+mA^2/(1+tan\[Beta]^2)-\[Mu]^2) gbMSSM[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]^2) Log[n],\[Mu]+1/(16 \[Pi]^2) \[Mu] (-(3/5) g1SM[Log[mtilde/MT]]^2-3 g2SM[Log[mtilde/MT]]^2+3 gbMSSM[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]^2+gtauMSSM[mtilde,mL3,mE3,M2,M1,\[Mu],tan\[Beta]]^2+3 gtMSSM[mtilde,tan\[Beta]]^2) Log[n],Xt+(-(1/(16 \[Pi]^2 tan\[Beta]))\[Mu] (-(3/5) g1SM[Log[mtilde/MT]]^2-3 g2SM[Log[mtilde/MT]]^2+3 gbMSSM[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt]^2+gtauMSSM[mtilde,mL3,mE3,M2,M1,\[Mu],tan\[Beta]]^2+3 gtMSSM[mtilde,tan\[Beta]]^2)+1/(120 \[Pi]^2) (13 M1 g1SM[Log[mtilde/MT]]^2+45 M2 g2SM[Log[mtilde/MT]]^2+80 M3 g3SM[Log[mtilde/MT]]^2+90 (Xt+\[Mu]/tan\[Beta]) gtMSSM[mtilde,tan\[Beta]]^2)+1/tan\[Beta] \[Mu] (-((g1SM[Log[mtilde/MT]]^2+3 g2SM[Log[mtilde/MT]]^2)/(64 \[Pi]^2))+(g1SM[Log[mtilde/MT]]^2+3 g2SM[Log[mtilde/MT]]^2-12 gtMSSM[mtilde,tan\[Beta]]^2)/(64 \[Pi]^2))) Log[n]};
XtOS[n_,mtilde_,Xt_]:=Xt+(Xt (8 g3SM[Log[mtilde/MT]]^2-3/2 gtSM[Log[mtilde/MT]]^2) Log[n])/(16 \[Pi]^2)]


(* ::Subsubsection::Closed:: *)
(*Calculation*)


Options[\[CapitalDelta]MhpoleHSSQ]={hiOrd->{1,1,1,1},scheme->"DR"};
\[CapitalDelta]MhpoleHSSQ[n_?positiveQ,mtilde_,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=If[OptionValue[scheme]=="OS",MhpoleHSS[n mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],XtOS[n,mtilde,Xt],opts]-MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,opts],
Block[{mQ32new,mU32new,mD32new,\[Mu]new,Xtnew},
{mQ32new,mU32new,mD32new,\[Mu]new,Xtnew}=spectrum[n,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt];
If[Not[mQ32new>0&&mU32new>0&&mD32new>0],Message[\[CapitalDelta]MHiggs::tachyon];Return[125]];
MhpoleHSS[n mtilde,mQ1,mQ2,Sqrt[mQ32new],mU1,mU2,Sqrt[mU32new],mD1,mD2,Sqrt[mD32new],mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu]new,M1,M2,M3,tan\[Beta],Xtnew,opts]-MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,opts]]]


Options[\[CapitalDelta]MhpoleHSSQfast]={hiOrd->{1,1,1,1},scheme->"DR"};
\[CapitalDelta]MhpoleHSSQfast[n_?positiveQ,mtilde_,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_,opts:OptionsPattern[]]:=If[OptionValue[scheme]=="OS",MhpoleHSSfast[n mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],XtOS[n,mtilde,Xt],opts]-MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,opts],
Block[{mQ32new,mU32new,mD32new,\[Mu]new,Xtnew},
{mQ32new,mU32new,mD32new,\[Mu]new,Xtnew}=spectrum[n,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt];
(*Print["spectrum","  ",n,"  ",Sqrt[mQ32new],"  ",Sqrt[mU32new],"  ",Sqrt[mD32new],"  ",\[Mu]new,"  ",Xtnew];*)
If[Not[mQ32new>0&&mU32new>0&&mD32new>0],Message[\[CapitalDelta]MHiggs::tachyon];Return[125]];
MhpoleHSSfast[n mtilde,mQ1,mQ2,Sqrt[mQ32new],mU1,mU2,Sqrt[mU32new],mD1,mD2,Sqrt[mD32new],mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu]new,M1,M2,M3,tan\[Beta],Xtnew,opts]-MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,opts]]]


(* ::Subsection::Closed:: *)
(*Sbottom contribution *)


\[CapitalDelta]MhpoleHSSbottom[mtilde_?positiveQ,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=If[tan\[Beta]<30,0,Abs[MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,1,1}]-MhpoleHSS[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0,1}]]]


\[CapitalDelta]MhpoleHSSbottomfast[mtilde_?positiveQ,mQ1_,mQ2_,mQ3_,mU1_,mU2_,mU3_,mD1_,mD2_,mD3_,mE1_,mE2_,mE3_,mL1_,mL2_,mL3_,mA_,\[Mu]_,M1_,M2_,M3_,tan\[Beta]_,Xt_]:=If[tan\[Beta]<30,0,Abs[MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,1,1}]-MhpoleHSSfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{0,0,0,1}]]]


(* ::Subsection::Closed:: *)
(*Total*)


Options[MhpoleHSSUnc]={hiOrd->{1,1,1,1},sources->{1,1,1},scheme->"DRbar"};
MhpoleHSSUnc[mtilde_?positiveQ,mQ1_?positiveQ,mQ2_?positiveQ,mQ3_?positiveQ,mU1_?positiveQ,mU2_?positiveQ,mU3_?positiveQ,mD1_?positiveQ,mD2_?positiveQ,mD3_?positiveQ,mE1_?positiveQ,mE2_?positiveQ,mE3_?positiveQ,mL1_?positiveQ,mL2_?positiveQ,mL3_?positiveQ,mA_?positiveQ,\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ,opts:OptionsPattern[]]:=
If[OptionValue[sources][[1]]==1,\[CapitalDelta]MhpoleHSSSM[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{scheme}]],0]+If[OptionValue[sources][[2]]==1,(Max[Abs@\[CapitalDelta]MhpoleHSSQ[2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],1,1,1}],Abs@\[CapitalDelta]MhpoleHSSQ[1/2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],1,1,1}],If[OptionValue[hiOrd][[2]]==0,Max[Abs@\[CapitalDelta]MhpoleHSSQ[2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],0,1,1}],Abs@\[CapitalDelta]MhpoleHSSQ[1/2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],0,1,1}]],0]   ]
+If[OptionValue[hiOrd][[3]]==0,\[CapitalDelta]MhpoleHSSbottom[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],0]),0]+If[OptionValue[sources][[3]]==1,\[CapitalDelta]MhpoleHSSmom[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],0]


Options[MhpoleHSSUncfast]={hiOrd->{1,1,1,1},sources->{1,1,1},scheme->"DRbar"};
MhpoleHSSUncfast[mtilde_?positiveQ,mQ1_?positiveQ,mQ2_?positiveQ,mQ3_?positiveQ,mU1_?positiveQ,mU2_?positiveQ,mU3_?positiveQ,mD1_?positiveQ,mD2_?positiveQ,mD3_?positiveQ,mE1_?positiveQ,mE2_?positiveQ,mE3_?positiveQ,mL1_?positiveQ,mL2_?positiveQ,mL3_?positiveQ,mA_?positiveQ,\[Mu]_?NumericQ,M1_?NumericQ,M2_?NumericQ,M3_?NumericQ,tan\[Beta]_?NumericQ,Xt_?NumericQ,opts:OptionsPattern[]]:=
If[OptionValue[sources][[1]]==1,\[CapitalDelta]MhpoleHSSSMfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{scheme}]],0]+If[OptionValue[sources][[2]]==1,(Max[Abs@\[CapitalDelta]MhpoleHSSQfast[2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],1,1,1},FilterRules[{opts},{scheme}]],Abs@\[CapitalDelta]MhpoleHSSQfast[1/2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],1,1,1},FilterRules[{opts},{scheme}]],If[OptionValue[hiOrd][[2]]==0,Max[Abs@\[CapitalDelta]MhpoleHSSQfast[2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],0,1,1},FilterRules[{opts},{scheme}]],Abs@\[CapitalDelta]MhpoleHSSQfast[1/2,mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,hiOrd->{OptionValue[hiOrd][[1]],0,1,1},FilterRules[{opts},{scheme}]]],0]   ]
+If[OptionValue[hiOrd][[3]]==0,\[CapitalDelta]MhpoleHSSbottomfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],0]),0]+If[OptionValue[sources][[3]]==1,\[CapitalDelta]MhpoleHSSmomfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt],0]


(* ::Subsection:: *)
(*\[CapitalDelta]MHiggs Function*)


Options[\[CapitalDelta]MHiggs]={hiOrd->{1,1,1,1},sources->{1,1,1},numerical->False,Rscale->0,scheme->"DR"};
\[CapitalDelta]MHiggs[shortList_?numericListQ,opts:OptionsPattern[]]:=Block[{tan\[Beta],M1,M2,M3,\[Mu],At,mQ3,mU3,mD3,mQ2,mU2,mD2,mQ1,mU1,mD1,mL3,mE3,mL2,mE2,mL1,mE1,mA,Xt,mtilde,msplit},
{tan\[Beta],M1,M2,M3,\[Mu],At,mQ3,mU3,mD3,mQ2,mU2,mD2,mQ1,mU1,mD1,mL3,mE3,mL2,mE2,mL1,mE1,mA}=getList[shortList];
If[NumericQ[tan\[Beta]]&&tan\[Beta]>=1&&cond[M1]&&cond[M2]&&cond[M3]&&cond[\[Mu]]&&Im[At]==0&&NumericQ[At]&&cond[mQ3]&&cond[mU3]&&cond[mD3]&&cond[mQ2]&&cond[mU2]&&cond[mD2]&&cond[mQ1]&&cond[mU1]&&cond[mD1]&&cond[mL3]&&cond[mE3]&&cond[mL2]&&cond[mE2]&&cond[mL1]&&cond[mE1]&&cond[mA],1,Message[MHiggs::variables];Return[0]];
Xt=At-\[Mu] /tan\[Beta];mtilde=If[OptionValue[Rscale]<200,Sqrt[mQ3 mU3],OptionValue[Rscale]];
If[Not[1/10<=mtilde/Sqrt[mQ3 mU3]<=10]||0<OptionValue[Rscale]<200,Message[MHiggs::warning]];
If[testgbDR[mtilde,mQ3,mU3,mD3,M3,\[Mu],tan\[Beta],Xt],Return[0]];
If[testgtauDR[mtilde,mL3,mE3,M2,M1,\[Mu],tan\[Beta]],Return[0]];
Which[
Not[OptionValue@numerical],
MhpoleHSSUncfast[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{hiOrd,sources,scheme}]],
OptionValue@numerical,
MhpoleHSSUnc[mtilde,mQ1,mQ2,mQ3,mU1,mU2,mU3,mD1,mD2,mD3,mE1,mE2,mE3,mL1,mL2,mL3,mA,\[Mu],M1,M2,M3,tan\[Beta],Xt,FilterRules[{opts},{hiOrd,sources}]]]];


End[]


EndPackage[]
