(* ::Package:: *)

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BeginPackage["SMPoleMatching`"];


Print["SMPoleMatching, v0.91, Mon 14 May 2012 12:02:46 F.Bezrukov <fedor@ms2.inr.ac.ru>"];


Off[General::spell1];


mZpole::usage="N[mZpole] gives the Z-boson pole mass M_Z";
mWpole::usage="N[mWpole] gives the W-boson pole mass M_W";
gF::usage="N[gF] gives the Fermi constant G_F";
alphaMZ::usage="N[alphaMZ] gives the fine structure constant alpha in MSbar scheme at MZ";
sw2MZ::usage="N[sw2MZ] gives the Sin^2 of Weinberg angle in MSbar scheme at MZ";
alpha137::usage="N[alpha] is the low energy fine structure constant 1/137";
sw2OS::usage="Is the on-shell Sin^2 of Weinberg angle defined via W and Z masses";


g10::usage="Symbol for the g_1 (or g') used in the returned ruled";
g20::usage="Symbol for the g_2 (or g) used in the returned ruled";
g30::usage="Symbol for the g_3 (or g_S) used in the returned ruled";
yt0::usage="Symbol for the y_t (top Yukawa) used in the returned ruled";
lambda0::usage="Symbol for the lambda (Higgs self coupling) used in the returned ruled";
mu0::usage="Symbol for mu (RG scale) used in the returned rules";


alphaS::usage="";
alphaS5::usage="";
alpha::usage="One loop running of the fine structure constant alpha";
gprime1loop::usage="One loop running of gprime";
g1loop::usage="One loop running of g";
gsQCD::usage="gsQCD[mt,aSMZ,mu] gives pure QCD 3-loop running of gs.  It is obtained by running from mZ to mt by 5-quark beta functions, and then solving from the mt to mu (even if mu<mt) by a 6-quark bta function.  Like this it is easier to use it for further high energy RG equation solving starting from mu!=mt";


constantsTree::usage="constantsTree[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} for the three level matching (and gauge constants at scale mu).  Best used with with mu=Mt.";
constantsQCD1::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 1-loop QCD matching for yt, 1-loop EW matching for yt and lambda.  Best used with with mu=Mt.";
constantsQCD2::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 2-loop QCD matching for yt, 1-loop EW matching for yt and lambda.  Best used with with mu=Mt.";
constantsQCD3::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda.  Best used with with mu=Mt.";
constantsQCD3top2::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for yt.  Best used with with mu=Mt.";
constantsQCD3higgs2::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for lambda.  Best used with with mu=Mt.";
constantsQCD3top2higgs2::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for yt and lambda.  Best used with with mu=Mt.";
constantsQCD3top2higgs3::usage="constantsQCD1[Mh,Mt,alphasMZ,mu] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for yt and lambda, O(yt^4) for lambda.  Best used with with mu=Mt.";


constantsQCD3top2higgs3Lin::usage="constantsQCD3top2higgs3Lin[Mh,Mt,alphasMZ,Mt] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for yt and lambda, O(yt^4) for lambda, USING LINEAR APPROXIMATION of all the analitic results.  Can be used only with with mu=Mt.";


constantsQCD3top2higgs3Linold::usage="constantsQCD3top2higgs3Lin[Mh,Mt,alphasMZ,Mt] gives the rule list {g10->#,g20->#,g30->#,yt0->0,lambda0->#,mu0->#} with values of the constant at mu, 3-loop QCD matching for yt, 1-loop EW matching for yt and lambda, 2-loop O(alpha alphaS) for yt and lambda, O(yt^4) for lambda, USING LINEAR APPROXIMATION of all the analitic results.  Can be used only with with mu=Mt.";


deltaMSGFa::usage="deltaMSGFa[mh,mt,alpha,mu] gives the barDelta G_{F,alpha} correction to G_F";
deltaMSGFaaS::usage="deltaMSGFaaS[mh,mt,alpha,aS,mu] gives the barDelta G_{F,alpha alpha_S} correction to G_F";


sigmaa::usage="sigmaa[Mh,Mt,alpha,mu] gives the sigma_alpha correction to the top mass";
sigmaaaS::usage="sigmaaaS[Mh,Mt,alpha,aS,mu] gives the sigma_{alpha alphaS} correction to the top mass";


deltaytaS::usage="deltaytaS[mt,aSMt,mu] O(alphaS) contribution to the top Yukawa. Use alphaS(Mt) for any mu!";
deltaytaSaS::usage="deltaytaSaS[mt,aSMt,mu] O(alphaS^2) contribution to the top Yukawa. Use alphaS(Mt) for any mu!";
deltaytaSaSaS::usage="deltaytaSaSaS[mt,aSMt,mu] O(alphaS^3) contribution to the top Yukawa. Use alphaS(Mt) for any mu!";
deltayta::usage="deltayta[mh,mt,alpha,mu] O(alpha) contribution to the top Yukawa.";
deltaytaaS::usage="deltaytaaS[mh,mt,alpha,aSmu,mu] O(alpha alphaS) contribution to the top Yukawa.";


deltaMSmha::usage="deltaMSmha[mh,mt,alpha,mu] delta_alpha contribution to the Higgs mass squared";
deltaMSmhaaS::usage="deltaMSmhaaS[mh,mt,alpha,aS,mu] delta_{alpha alphaS} contribution to the Higgs mass squared";


deltaha::usage="deltaha[mh,mt,alpha,mu] O(alpha) contribution to the Higgs coupling";
deltahaaS::usage="deltahaaS[mh,mt,alpha,aS,mu] O(alpha alphaS) contribution to the Higgs coupling";
deltahy6::usage="deltahy6[mh,mt,mu] O(yt^4) contribution to the Higgs coupling from 1205.6497";
deltahaaSDgsi::usage="deltahaaSDgsi[mh,mt,aS,mu] analogue of deltahaaS from 1205.6497";


Begin["`Private`"]


N[mZpole]=91.1876 (* (21)GeV *);
N[mWpole]=80.399 (* (23) GeV *);
N[gF]=1.16637*10^-5 (* (1) GeV^-2 *);
N[alphaMZ]=127.916^-1 (* (0.015) *);
N[sw2MZ]=0.23116 (* (13) *);


N[alpha137]=1/137.035999679(*94*);


vev:=Sqrt[1/(Sqrt[2]gF)];
sw2OS:=1-(mWpole/mZpole)^2;


alpha[mu_]=Module[{b1,b1p,ng=3},
b1=-22/3+4/3*ng+1/6;
b1p=(4/3*ng+1/10)*5/3;
alphaMZ/(1-(b1+b1p)/(2\[Pi]) alphaMZ Log[mu/mZpole])]


Module[{b1,b1p,ng=3},
b1=-22/3+4/3*ng+1/6;
b1p=(4/3*ng+1/10)*5/3;
{b1,b1p,b1+b1p,alphaMZ/(1-(b1+b1p)/(2\[Pi]) alphaMZ Log[mu/mZpole])}]


g1loop[mu_]=Module[{b1,ng=3,gMZ=Sqrt[(4\[Pi] alphaMZ)/sw2MZ]},
b1=-22/3+4/3*ng+1/6;
gMZ/Sqrt[1-b1/(8\[Pi]^2) gMZ^2 Log[mu/mZpole]]];
gprime1loop[mu_]=Module[{b1p,ng=3,gpMZ=Sqrt[(4\[Pi] alphaMZ)/(1-sw2MZ)]},
b1p=(4/3*ng+1/10)*5/3;
gpMZ/Sqrt[1-b1p/(8\[Pi]^2) gpMZ^2 Log[mu/mZpole]]];


alphaS[aS0_,mu0_,mu_,nf_]:=With[{b0=11-2/3 nf,b1=51-19/3 nf,b2=2857-5033/9 nf+325/27 nf^2},a[Log[mu/mu0]]/.First[NDSolve[{a'[t]==-(b0/(2\[Pi])) a[t]^2-b1/(4\[Pi]^2) a[t]^3-b2/(64\[Pi]^3) a[t]^4,a[0]==aS0},a,{t,0,Log[mu/mu0]}]]//N]


alphaStopmatch[aSnf1_]=aSnf1-11/(72\[Pi]^2) aSnf1^3;


alphaS5[aSMZ_,mu_]:=alphaS[aSMZ,mZpole,mu,5]


gsQCD[mt_,aSMZ_,mt_]:=Sqrt[4\[Pi] alphaStopmatch[alphaS[aSMZ,mZpole,mt,5]]]
gsQCD[mt_,aSMZ_,mu_]:=Sqrt[4\[Pi] alphaS[alphaStopmatch[alphaS[aSMZ,mZpole,mt,5]],mt,mu,6]]


deltaMSGFa[mh_,mt_,alpha_,mu_]=With[{sinOS=sw2OS,MMu3=mt^2,MMW=mWpole^2,MMH=mh^2,mm=mu^2,MMZ=mZpole^2},
alpha/(4*Pi)*1/sinOS*(-5/4+3/4*MMu3*MMW^(-1)-6*MMu3^2*MMH^(-1)*MMW^(-1)+1/2*MMH^(-1)*MMZ^2*MMW^(-1)+MMH^(-1)*MMW+7/8*MMH*MMW^(-1)-5/8*MMZ*MMW^(-1)+3/4/(MMH-MMW)*Log[MMH*mm^(-1)]*MMW-3/4/(MMH-MMW)*Log[MMW*mm^(-1)]*MMW-3/2*Log[MMu3*mm^(-1)]*MMu3*MMW^(-1)+6*Log[MMu3*mm^(-1)]*MMu3^2*MMH^(-1)*MMW^(-1)+3/4*Log[MMH*mm^(-1)]-3/4*Log[MMH*mm^(-1)]*MMH*MMW^(-1)+7/2*Log[MMZ*mm^(-1)]*sinOS^(-1)-3/2*Log[MMZ*mm^(-1)]*MMH^(-1)*MMZ^2*MMW^(-1)-17/4*Log[MMZ*mm^(-1)]*MMZ*MMW^(-1)*sinOS^(-1)+5*Log[MMZ*mm^(-1)]*MMZ*MMW^(-1)+3/4*Log[MMW*mm^(-1)]-7/2*Log[MMW*mm^(-1)]*sinOS^(-1)-3*Log[MMW*mm^(-1)]*MMH^(-1)*MMW+17/4*Log[MMW*mm^(-1)]*MMZ*MMW^(-1)*sinOS^(-1)-17/4*Log[MMW*mm^(-1)]*MMZ*MMW^(-1))
];


deltaMSGFaaS[mh_,mt_,alpha_,alphaS_,mu_]=With[{sinOS=sw2OS,MMu3=mt^2,MMW=mWpole^2,MMH=mh^2,mm=mu^2},
alpha/(4*Pi)*alphaS/(4*Pi)*1/sinOS*(29/2*MMu3*MMW^(-1)-16*MMu3^2*MMH^(-1)*MMW^(-1)-4*Zeta[2]*MMu3*MMW^(-1)+6*Log[MMu3*mm^(-1)]*MMu3*MMW^(-1)-96*Log[MMu3*mm^(-1)]*MMu3^2*MMH^(-1)*MMW^(-1)-6*Log[MMu3*mm^(-1)]*Log[MMu3*mm^(-1)]*MMu3*MMW^(-1)+48*Log[MMu3*mm^(-1)]*Log[MMu3*mm^(-1)]*MMu3^2*MMH^(-1)*MMW^(-1))
];


funcZ[z_]:=If[z>1/4,
With[{a=Sqrt[4z-1]},2a ArcTan[1/a]],
With[{a=Sqrt[1-4z]},a Log[(1+a)/(1-a)]]]


PR123[mm1_?NumericQ,mm2_?NumericQ,mm3_?NumericQ,mm_?NumericQ]:=NIntegrate[Log[ mm3/mm*x*(x-1) + mm2/mm*x + mm1/mm*(1-x) -I*10^(-80)],{x,0,1},Exclusions->mm3/mm*x*(x-1) + mm2/mm*x + mm1/mm*(1-x)==0];


PR123[mm1_?NumericQ,mm1_?NumericQ,mm3_?NumericQ,mm_?NumericQ]:=funcZ[mm1/mm3]-2+Log[mm1/mm];


deltaMSmhaFull[mh_,mt_,alpha_,mu_]=With[{sinOS=sw2OS,
mme1=(0.51/1000)^2,mme2=(105.6583/1000)^2,mme3=(1777.03/1000)^2,mmd1=(6/1000)^2,mmd2=(120/1000)^2,mmd3=(4.4)^2,
mmu1=(3/1000)^2,mmu2=(1.2)^2,MMu3=(mt)^2,
MMW=(mWpole)^2,MMZ=(mZpole)^2,
MMH=mh^2,
mm=mu^2},
alpha/(4*Pi)*1/sinOS*(+mme1*(-1/2*PR123[mme1,mme1,MMH,mm]*MMW^(-1))+mme1^2*(2*MMH^(-1)*MMW^(-1)-2*Log[mm^(-1)*mme1]*MMH^(-1)*MMW^(-1)+2*PR123[mme1,mme1,MMH,mm]*MMH^(-1)*MMW^(-1))+mme2*(-1/2*PR123[mme2,mme2,MMH,mm]*MMW^(-1))+mme2^2*(2*MMH^(-1)*MMW^(-1)-2*Log[mm^(-1)*mme2]*MMH^(-1)*MMW^(-1)+2*PR123[mme2,mme2,MMH,mm]*MMH^(-1)*MMW^(-1))+mme3*(-1/2*PR123[mme3,mme3,MMH,mm]*MMW^(-1))+mme3^2*(2*MMH^(-1)*MMW^(-1)-2*Log[mm^(-1)*mme3]*MMH^(-1)*MMW^(-1)+2*PR123[mme3,mme3,MMH,mm]*MMH^(-1)*MMW^(-1))+mmu1*(-3/2*PR123[mmu1,mmu1,MMH,mm]*MMW^(-1))+mmu1^2*(6*MMH^(-1)*MMW^(-1)-6*Log[mm^(-1)*mmu1]*MMH^(-1)*MMW^(-1)+6*PR123[mmu1,mmu1,MMH,mm]*MMH^(-1)*MMW^(-1))+mmu2*(-3/2*PR123[mmu2,mmu2,MMH,mm]*MMW^(-1))+mmu2^2*(6*MMH^(-1)*MMW^(-1)-6*Log[mm^(-1)*mmu2]*MMH^(-1)*MMW^(-1)+6*PR123[mmu2,mmu2,MMH,mm]*MMH^(-1)*MMW^(-1))+mmd1*(-3/2*PR123[mmd1,mmd1,MMH,mm]*MMW^(-1))+mmd1^2*(6*MMH^(-1)*MMW^(-1)-6*Log[mm^(-1)*mmd1]*MMH^(-1)*MMW^(-1)+6*PR123[mmd1,mmd1,MMH,mm]*MMH^(-1)*MMW^(-1))+mmd2*(-3/2*PR123[mmd2,mmd2,MMH,mm]*MMW^(-1))+mmd2^2*(6*MMH^(-1)*MMW^(-1)-6*Log[mm^(-1)*mmd2]*MMH^(-1)*MMW^(-1)+6*PR123[mmd2,mmd2,MMH,mm]*MMH^(-1)*MMW^(-1))+mmd3*(-3/2*PR123[mmd3,mmd3,MMH,mm]*MMW^(-1))+mmd3^2*(6*MMH^(-1)*MMW^(-1)-6*Log[mm^(-1)*mmd3]*MMH^(-1)*MMW^(-1)+6*PR123[mmd3,mmd3,MMH,mm]*MMH^(-1)*MMW^(-1))-1/2-3/2*MMH^(-1)*MMW^(-1)*MMZ^2+6*MMH^(-1)*MMW^(-1)*MMu3^2-3*MMH^(-1)*MMW+3/2*MMH*MMW^(-1)-1/4*MMW^(-1)*MMZ-9/8/(Sqrt[3])*Pi*MMH*MMW^(-1)-3/8*Log[MMH*mm^(-1)]*MMH*MMW^(-1)+1/2*Log[MMW*mm^(-1)]+3*Log[MMW*mm^(-1)]*MMH^(-1)*MMW+3/2*Log[MMZ*mm^(-1)]*MMH^(-1)*MMW^(-1)*MMZ^2+1/4*Log[MMZ*mm^(-1)]*MMW^(-1)*MMZ-6*Log[MMu3*mm^(-1)]*MMH^(-1)*MMW^(-1)*MMu3^2+PR123[MMW,MMW,MMH,mm]-3*PR123[MMW,MMW,MMH,mm]*MMH^(-1)*MMW-1/4*PR123[MMW,MMW,MMH,mm]*MMH*MMW^(-1)-3/2*PR123[MMZ,MMZ,MMH,mm]*MMH^(-1)*MMW^(-1)*MMZ^2-1/8*PR123[MMZ,MMZ,MMH,mm]*MMH*MMW^(-1)+1/2*PR123[MMZ,MMZ,MMH,mm]*MMW^(-1)*MMZ+6*PR123[MMu3,MMu3,MMH,mm]*MMH^(-1)*MMW^(-1)*MMu3^2-3/2*PR123[MMu3,MMu3,MMH,mm]*MMW^(-1)*MMu3)];


deltaMSmha[mh_,mt_,alpha_,mu_]=With[{sinOS=sw2OS,
MMu3=(mt)^2,
MMW=(mWpole)^2,MMZ=(mZpole)^2,
MMH=mh^2,
mm=mu^2},
alpha/(4*Pi)*1/sinOS*(-1/2
-3/2*MMH^(-1)*MMW^(-1)*MMZ^2+6*MMH^(-1)*MMW^(-1)*MMu3^2-3*MMH^(-1)*MMW+3/2*MMH*MMW^(-1)-1/4*MMW^(-1)*MMZ-9/8/(Sqrt[3])*Pi*MMH*MMW^(-1)-3/8*Log[MMH*mm^(-1)]*MMH*MMW^(-1)+1/2*Log[MMW*mm^(-1)]+3*Log[MMW*mm^(-1)]*MMH^(-1)*MMW+3/2*Log[MMZ*mm^(-1)]*MMH^(-1)*MMW^(-1)*MMZ^2+1/4*Log[MMZ*mm^(-1)]*MMW^(-1)*MMZ-6*Log[MMu3*mm^(-1)]*MMH^(-1)*MMW^(-1)*MMu3^2+PR123[MMW,MMW,MMH,mm]-3*PR123[MMW,MMW,MMH,mm]*MMH^(-1)*MMW-1/4*PR123[MMW,MMW,MMH,mm]*MMH*MMW^(-1)-3/2*PR123[MMZ,MMZ,MMH,mm]*MMH^(-1)*MMW^(-1)*MMZ^2-1/8*PR123[MMZ,MMZ,MMH,mm]*MMH*MMW^(-1)+1/2*PR123[MMZ,MMZ,MMH,mm]*MMW^(-1)*MMZ+6*PR123[MMu3,MMu3,MMH,mm]*MMH^(-1)*MMW^(-1)*MMu3^2-3/2*PR123[MMu3,MMu3,MMH,mm]*MMW^(-1)*MMu3)];


deltaMSmhaaS[mh_,mt_,alpha_,alphaS_,mu_]:=With[{sinOS=sw2OS,MMu3=mt^2,MMW=mWpole^2,MMH=mh^2,mm=mu^2,
y=(Sqrt[1-4*(mt/mh)^2+I*10^(-80)]-1)/(Sqrt[1-4*(mt/mh)^2+I*10^(-80)]+1)},
alpha/(4*Pi)*alphaS/(4*Pi)*1/sinOS*MMu3^2*1/MMW*1/MMH*(-1-67/2*y^(-1)-67/2*y-512/(1-2*y+y^2)*PolyLog[2,-y]*Log[y]-256/(1-2*y+y^2)*PolyLog[2,y]*Log[y]+768/(1-2*y+y^2)*PolyLog[3,-y]+384/(1-2*y+y^2)*PolyLog[3,y]+192/(1-2*y+y^2)*Zeta[3]-52/(1-2*y+y^2)*Log[y]*Log[y]-64/(1-2*y+y^2)*Log[y]*Log[y]*Log[1-y]-128/(1-2*y+y^2)*Log[y]*Log[y]*Log[1+y]+128/(1-y)/(1+y)*Log[y]*y-96/(1-y)/(1+y)*Log[y]*Log[ MMu3*mm^(-1)]*y+256/(1-y)*PolyLog[2,-y]+512/(1-y)*PolyLog[2,-y]*Log[y]+128/(1-y)*PolyLog[2,y]+256/(1-y)*PolyLog[2,y]*Log[y]-768/(1-y)*PolyLog[3,-y]-384/(1-y)*PolyLog[3,y]-192/(1-y)*Zeta[3]-360/(1-y)*Log[y]+128/(1-y)*Log[y]*y+128/(1-y)*Log[y]*Log[1-y]+256/(1-y)*Log[y]*Log[1+y]+144/(1-y)*Log[y]*Log[ MMu3*mm^(-1)]-96/(1-y)*Log[y]*Log[ MMu3*mm^(-1)]*y-44/(1-y)*Log[y]*Log[y]+64/(1-y)*Log[y]*Log[y]*Log[1-y]+128/(1-y)*Log[y]*Log[y]*Log[1+y]+32/(1+y)*Log[y]-32/(1+y)*Log[y]*y-24/(1+y)*Log[y]*Log[ MMu3*mm^(-1)]+24/(1+y)*Log[y]*Log[ MMu3*mm^(-1)]*y-128*PolyLog[2,-y]+32*PolyLog[2,-y]*y^(-1)-32*PolyLog[2,-y]*y-256*PolyLog[2,-y]*Log[y]-64*PolyLog[2,-y]*Log[y]*y^(-1)-64*PolyLog[2,-y]*Log[y]*y-64*PolyLog[2,y]+16*PolyLog[2,y]*y^(-1)-16*PolyLog[2,y]*y-128*PolyLog[2,y]*Log[y]-32*PolyLog[2,y]*Log[y]*y^(-1)-32*PolyLog[2,y]*Log[y]*y+384*PolyLog[3,-y]+96*PolyLog[3,-y]*y^(-1)+96*PolyLog[3,-y]*y+192*PolyLog[3,y]+48*PolyLog[3,y]*y^(-1)+48*PolyLog[3,y]*y+96*Zeta[3]+24*Zeta[3]*y^(-1)+24*Zeta [3]*y+12*Log [MMu3*mm^(-1)]-6*Log[ MMu3*mm^(-1)]*y^(-1)-6*Log[MMu3*mm^(-1)]*y-12*Log[ MMu3*mm^(-1)]*Log[ MMu3*mm^(-1)]+6*Log[ MMu3*mm^(-1)]*Log[ MMu3*mm^(-1)]*y^(-1)+6*Log[ MMu3*mm^(-1)]*Log[ MMu3*mm^(-1)]*y+244*Log[y]-18*Log[y]*y^(-1)+18*Log[y]*y-64*Log[y]*Log[1-y]+16*Log[y]*Log[1-y]*y^(-1)-16*Log[y]*Log[1-y]*y-128*Log[y]*Log[1+y]+32*Log[y]*Log[1+y]*y^(-1)-32*Log[y]*Log[1+y]*y-120*Log[y]*Log[ MMu3*mm^(-1)]+44*Log[y]*Log[y]-6*Log[y]*Log[y]*y^(-1)+18*Log[y]*Log[y]*y-32*Log[y]*Log[y]*Log[1-y]-8*Log[y]*Log[y]*Log[1-y]*y^(-1)-8*Log[y]*Log[y]*Log[1-y]*y-64*Log[y]*Log[y]*Log[1+y]-16*Log[y]*Log[y]*Log[1+y]*y^(-1)-16*Log[y]*Log[y]*Log[1+y]*y)
];


deltaha[mh_,mt_,a_,mu_]:=Re[deltaMSmha[mh,mt,a,mu]]+deltaMSGFa[mh,mt,a,mu]


deltahaaS[mh_,mt_,a_,aS_,mu_]:=Re[deltaMSmhaaS[mh,mt,a,aS,mu]]+deltaMSGFaaS[mh,mt,a,aS,mu]


b0[mh_,mh_,mh_,mu_]:=With[{lh=Log[mh^2/mu^2]},2-lh-\[Pi]/Sqrt[3]]
b0[m1_,m2_,m3_,mu_]:=-PR123[m1,m2,m3,mu]


deltahaaSDgsi[mh_,mt_,as_,mu_]:=With[{nc=3,lt=Log[mt^2/mu^2],lh=Log[mh^2/mu^2],xht=mh^2/mt^2,s2=0.260434138,cf=4/3,gs2=4\[Pi] as},(2/(Sqrt[2]gF mh^2))
((gF^2 mt^4)/(4\[Pi])^4 nc cf gs2(16(-4-6lt+3lt^2)
+xht(35-(2\[Pi]^2)/3+12lt-12lt^2)+xht^2 61/135+xht^3 1223/6300+xht^4 43123/1323000
))]


deltahy6[mh_,mt_,mu_]:=With[{nc=3,lt=Log[mt^2/mu^2],lh=Log[mh^2/mu^2],xht=mh^2/mt^2,s2=0.260434138},(2/(Sqrt[2]gF mh^2))
((Sqrt[2] gF^3 mt^6)/(4\[Pi])^4 (
nc^2 (16b0[mt,mt,mh,mu](-1+2lt)
+xht((1+4b0[mt,mt,mh,mu]-2lt)(1-2lt)))
+nc(16+8/3 \[Pi]^2+32b0[mt,mh,mt,mu](1+2lt)-48lt+40lt^2
-xht(929/6+16/3 \[Pi]^2+48b0[mh,mh,mh,mu]-16lh(1-lt)
+b0[mt,mh,mt,mu](76/3+32lt)+190/3 lt+58lt^2)
+xht^2 (17629/270+8/3 \[Pi]^2-2/3 lh+b0[mh,mh,mh,mu](27-18lt)+40lt
+10lt lh+12lt^2+b0[mt,mh,mt,mu](13/3+4lt))
+xht^3 (1181/900-\[Pi]^2/2+61/30 b0[mh,mh,mh,mu]+59/90 lh
-2/35 b0[mt,mh,mt,mu]-68/63 lt))
+xht^3 (131/6 \[Pi]^2+(729/2-135/4 Sqrt[3]\[Pi])s2-111lh+36lh^2
+\[Pi]((-225 Sqrt[3])/4+18Sqrt[3]lh)+(75+72Zeta[3])/4)
))]


sigmaa[Mh_,Mt_,alpha_,Mt_]:=With[{MW=mWpole,MZ=mZpole,YH=(1-Sqrt[1-(4 Mt^2)/Mh^2-I/10^80])/(1+Sqrt[1-(4 Mt^2)/Mh^2-I/10^80])},
-(alpha/(4\[Pi] sw2OS))(0.3747795+1/2 MW^2/Mh^2 (1-3Log[MW^2/Mt^2])
-3/4 MZ^4/(MW^2 Mh^2) Log[MZ^2/Mt^2]+Mt^4/(MW^2 Mh^2) (1/2 Mh^2/Mt^2 (1+YH^2)/YH+1/4 MZ^4/Mt^4-3)
-1/8 Mh^4/(Mt^2 MW^2) Log[1+YH]+1/8 Mh^2/MW^2 (3+YH^2)/(1+YH) Log[YH])
];


sigmaa[Mh_,Mt_,alpha_,mu_]:=With[{s=sw2OS,
mme1=(0.51/1000)^2,mme2=(105.6583/1000)^2,mme3=(1777.03/1000)^2,mmd1=(6/1000)^2,mmd2=(120/1000)^2,mmd3=(4.4)^2,
mmu1=(3/1000)^2,mmu2=(1.2)^2,mmu3=(Mt)^2,
mmW=(mWpole)^2,mmZ=(mZpole)^2,
mmH=Mh^2,
mm=mu^2},
alpha/(4Pi)/s*1/2(+ mme1^2*mmW^(-1)*mmH^(-1) * ( 2 - 2*Log[(mm^(-1)*mmZ)] - 2*Log[(mme1*mmZ^(-1))] )
+ mme2^2*mmW^(-1)*mmH^(-1) * ( 2 - 2*Log[(mm^(-1)*mmZ)] - 2*Log[(mme2*mmZ^(-1))] )
+ mme3^2*mmW^(-1)*mmH^(-1) * ( 2 - 2*Log[(mm^(-1)*mmZ)] - 2*Log[(mme3*mmZ^(-1))] )
+ mmW^(-1)*mmH^(-1)*mmu1^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmu1)] )
+ mmW^(-1)*mmH^(-1)*mmu2^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmu2)] )
+ mmW^(-1)*mmH^(-1)*mmu3^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmu3)] )
+ mmW^(-1)*mmH^(-1)*mmd1^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmd1)] )
+ mmW^(-1)*mmH^(-1)*mmd2^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmd2)] )
+ mmW^(-1)*mmH^(-1)*mmd3^2 * ( 6 - 6*Log[(mm^(-1)*mmZ)] - 6*Log[(mmZ^(-1)*mmd3)] )
+ mmW^(-1)*mmZ * (  - 1/2 + 2/3*Log[(mm^(-1)*mmZ)] + 17/36*Log[(mmZ^(-1)*mmu3)] + 7/36*PR123[mmZ,mmu3,mmu3,mmZ] )
+ mmW^(-1)*mmZ^2*mmH^(-1) * (  - 1/2 + 3/2*Log[(mm^(-1)*mmZ)] )
+ mmW^(-1)*mmZ^2*mmu3^(-1) * ( 17/36 + 17/36*PR123[mmZ,mmu3,mmu3,mmZ] )
+ mmW^(-1)*mmH * (  - 1/2 + 3/4*Log[(mm^(-1)*mmZ)] + 1/2*Log[(mmZ^(-1)*mmH)]+ 1/4*PR123[mmH,mmu3,mmu3,mmZ] )
+ mmW^(-1)*mmu3^(-1)*mmd3^2 * (  - 1/4 + 1/4*Log[(mmZ^(-1)*mmd3)] - 1/4*PR123[mmd3,mmW,mmu3,mmZ] )
+ mmW^(-1)*mmu3 * (  - 1/2 - 3/4*Log[(mm^(-1)*mmZ)] + 1/2*Log[(mmZ^(-1)*mmu3)]- PR123[mmH,mmu3,mmu3,mmZ] - 1/4*PR123[mmd3,mmW,mmu3,mmZ] )
+ mmW^(-1)*mmd3 * (  - 1/4 + 3/4*Log[(mm^(-1)*mmZ)] + 1/4*Log[(mmZ^(-1)*mmd3)]+ 1/2*PR123[mmd3,mmW,mmu3,mmZ] )
+ mmW*mmZ^(-1) * ( 32/9 - 16/9*Log[(mmZ^(-1)*mmu3)] + 16/9*PR123[mmZ,mmu3,mmu3,mmZ] )
+ mmW*mmH^(-1) * (  - 1 + 3*Log[(mm^(-1)*mmZ)] + 3*Log[(mmW*mmZ^(-1))] )
+ mmW*mmu3^(-1) * ( 25/18 - 1/2*Log[(mmW*mmZ^(-1))] + 8/9*PR123[mmZ,mmu3,mmu3,mmZ] + 1/2*PR123[mmd3,mmW,mmu3,mmZ] )
+ mmZ*mmu3^(-1) * (  - 10/9 - 10/9*PR123[mmZ,mmu3,mmu3,mmZ] )
+ mmu3^(-1)*mmd3 * (  - 1/4 - 1/4*Log[(mmW*mmZ^(-1))] + 1/2*Log[(mmZ^(-1)*mmd3)] - 1/4*PR123[mmd3,mmW,mmu3,mmZ] )
- 155/36
- 2/3*Log[(mm^(-1)*mmZ)]
+ 1/4*Log[(mmW*mmZ^(-1))]
+ 14/9*Log[(mmZ^(-1)*mmu3)]
- 20/9*PR123[mmZ,mmu3,mmu3,mmZ]
- 1/4*PR123[mmd3,mmW,mmu3,mmZ])];


sigmaaaS[mH_,mt_,alpha_,alphaS_,mt_]:=With[{
Cf=4/3,
mmH=mH^2,mmu3=mt^2,
mmW=mWpole^2,mmZ=mZpole^2,sw2=sw2OS,
tw=mt^2/mWpole^2,YZ=(1-Sqrt[1-(4 mt^2)/mZpole^2-I/10^80])/(1+Sqrt[1-(4 mt^2)/mZpole^2-I/10^80]),YH=(1-Sqrt[1-(4 mt^2)/mH^2-I/10^80])/(1+Sqrt[1-(4 mt^2)/mH^2-I/10^80])},
-Cf alphaS/(4\[Pi]) alpha/(4\[Pi] sw2) (-78.591+6 mmW/mmH Log[mmW/mmu3]+3 mmZ^2/(mmW mmH) Log[mmZ/mmu3]-2 mmW/mmH
+mmu3^2/(mmH mmW) (-11/8 mmH/mmu3 (1+YH^2)/YH-mmZ^2/mmu3^2+6)+Zeta[2] mmu3/mmW (3/(2YH)+9/2 YH+3/4 YH^2)
+mmu3/mmW (1-YH)^2/YH^2 Log[YH](Log[1-YH]+1/2 Log[1+YH])((1-YH^2)-1/2 (1+YH^2)Log[YH])
-1/8 mmu3/mmW (2+8YH-10YH^2-3YH^3)/YH Log[YH]^2+1/8 mmu3/mmW (1+YH)(11YH-39)Log[YH]
-1/8 mmH/mmW (11-50YH+11YH^2)/YH Log[1+YH]-3/2 mmu3/mmW Zeta[2]Log[1+YH] ((1-YH)^2 (1+YH^2))/YH^2
+mmu3/mmW ((1-YH)(1+YH))/YH^2 ((5-28YH+5YH^2)/4 PolyLog[2,-YH]+(1-YH)^2 PolyLog[2,YH])
+mmu3/mmW ((1-YH)^2 (1+YH^2))/YH^2 (3/2 (2PolyLog[3,YH]+PolyLog[3,-YH])-Log[YH](2PolyLog[2,YH]+PolyLog[2,-YH])))]


sigmaaaS[mH_,mt_,alpha_,alphaS_,mu_]:=With[{
mmH=mH^2,mmu3=mt^2,mm=mu^2,
mmW=mWpole^2,mmZ=mZpole^2,sw2=sw2OS,
tw=mt^2/mWpole^2,YZ=(1-Sqrt[1-(4 mt^2)/mZpole^2-I/10^80])/(1+Sqrt[1-(4 mt^2)/mZpole^2-I/10^80]),YH=(1-Sqrt[1-(4 mt^2)/mH^2-I/10^80])/(1+Sqrt[1-(4 mt^2)/mH^2-I/10^80])},
 alphaS/(4\[Pi]) alpha/(4\[Pi] sw2) (-(449/36)+275/(27 tw)+(11 tw)/(6 YH)+(11 tw YH)/6+(187 tw)/(54 YZ^2)+(1121 tw)/(72 YZ)+(1121 tw YZ)/72+(187 tw YZ^2)/54+(1969 tw)/54-220/(27 YZ)-(220 YZ)/27+8/((3 (1+YH)) tw)+(4 tw)/((3 (1+YH)) YZ^2)+(16 tw)/((3 (1+YH)) YZ)+(16 tw YZ)/(3 (1+YH))+(4 tw YZ^2)/(3 (1+YH))-(8 Log[1+YZ] tw)/((1+YH) YZ^2)-(32 Log[1+YZ] tw)/((1+YH) YZ)-(32 Log[1+YZ] tw YZ)/(1+YH)-(8 Log[1+YZ] tw YZ^2)/(1+YH)-(48 Log[1+YZ] tw)/(1+YH)-(8 Log[1/tw])/((1+YH) tw)+(6 Log[1/tw] Log[mmu3/mm])/((1+YH) tw)-(10 Log[mmu3/mm])/((1+YH) tw)-(5 Log[mmu3/mm] tw)/((1+YH) YZ^2)-(20 Log[mmu3/mm] tw)/((1+YH) YZ)-(20 Log[mmu3/mm] tw YZ)/(1+YH)-(5 Log[mmu3/mm] tw YZ^2)/(1+YH)+(46 Log[mmu3/mm] tw)/(1+YH)+(6 Log[mmu3/mm] Log[1+YZ] tw)/((1+YH) YZ^2)+(24 Log[mmu3/mm] Log[1+YZ] tw)/((1+YH) YZ)+(24 Log[mmu3/mm] Log[1+YZ] tw YZ)/(1+YH)+(6 Log[mmu3/mm] Log[1+YZ] tw YZ^2)/(1+YH)+(36 Log[mmu3/mm] Log[1+YZ] tw)/(1+YH)+(6 Log[mmu3/mm] Log[mmu3/mm])/((1+YH) tw)+(3 Log[mmu3/mm] Log[mmu3/mm] tw)/((1+YH) YZ^2)+(12 Log[mmu3/mm] Log[mmu3/mm] tw)/((1+YH) YZ)+(12 Log[mmu3/mm] Log[mmu3/mm] tw YZ)/(1+YH)+(3 Log[mmu3/mm] Log[mmu3/mm] tw YZ^2)/(1+YH)-(18 Log[mmu3/mm] Log[mmu3/mm] tw)/(1+YH)+(4 Log[YZ] tw)/((1+YH) YZ^2)+(16 Log[YZ] tw)/((1+YH) YZ)+(16 Log[YZ] tw YZ)/(1+YH)+(4 Log[YZ] tw YZ^2)/(1+YH)+(24 Log[YZ] tw)/(1+YH)-(3 Log[YZ] Log[mmu3/mm] tw)/((1+YH) YZ^2)-(12 Log[YZ] Log[mmu3/mm] tw)/((1+YH) YZ)-(12 Log[YZ] Log[mmu3/mm] tw YZ)/(1+YH)-(3 Log[YZ] Log[mmu3/mm] tw YZ^2)/(1+YH)-(18 Log[YZ] Log[mmu3/mm] tw)/(1+YH)-8/((3 (1+2 YH+YH^2)) tw)-(4 tw)/((3 (1+2 YH+YH^2)) YZ^2)-(16 tw)/((3 (1+2 YH+YH^2)) YZ)-(16 tw YZ)/(3 (1+2 YH+YH^2))-(4 tw YZ^2)/(3 (1+2 YH+YH^2))+(8 Log[1+YZ] tw)/((1+2 YH+YH^2) YZ^2)+(32 Log[1+YZ] tw)/((1+2 YH+YH^2) YZ)+(32 Log[1+YZ] tw YZ)/(1+2 YH+YH^2)+(8 Log[1+YZ] tw YZ^2)/(1+2 YH+YH^2)+(48 Log[1+YZ] tw)/(1+2 YH+YH^2)+(8 Log[1/tw])/((1+2 YH+YH^2) tw)-(6 Log[1/tw] Log[mmu3/mm])/((1+2 YH+YH^2) tw)+(10 Log[mmu3/mm])/((1+2 YH+YH^2) tw)+(5 Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ^2)+(20 Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ)+(20 Log[mmu3/mm] tw YZ)/(1+2 YH+YH^2)+(5 Log[mmu3/mm] tw YZ^2)/(1+2 YH+YH^2)-(46 Log[mmu3/mm] tw)/(1+2 YH+YH^2)-(6 Log[mmu3/mm] Log[1+YZ] tw)/((1+2 YH+YH^2) YZ^2)-(24 Log[mmu3/mm] Log[1+YZ] tw)/((1+2 YH+YH^2) YZ)-(24 Log[mmu3/mm] Log[1+YZ] tw YZ)/(1+2 YH+YH^2)-(6 Log[mmu3/mm] Log[1+YZ] tw YZ^2)/(1+2 YH+YH^2)-(36 Log[mmu3/mm] Log[1+YZ] tw)/(1+2 YH+YH^2)-(6 Log[mmu3/mm] Log[mmu3/mm])/((1+2 YH+YH^2) tw)-(3 Log[mmu3/mm] Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ^2)-(12 Log[mmu3/mm] Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ)-(12 Log[mmu3/mm] Log[mmu3/mm] tw YZ)/(1+2 YH+YH^2)-(3 Log[mmu3/mm] Log[mmu3/mm] tw YZ^2)/(1+2 YH+YH^2)+(18 Log[mmu3/mm] Log[mmu3/mm] tw)/(1+2 YH+YH^2)-(4 Log[YZ] tw)/((1+2 YH+YH^2) YZ^2)-(16 Log[YZ] tw)/((1+2 YH+YH^2) YZ)-(16 Log[YZ] tw YZ)/(1+2 YH+YH^2)-(4 Log[YZ] tw YZ^2)/(1+2 YH+YH^2)-(24 Log[YZ] tw)/(1+2 YH+YH^2)+(3 Log[YZ] Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ^2)+(12 Log[YZ] Log[mmu3/mm] tw)/((1+2 YH+YH^2) YZ)+(12 Log[YZ] Log[mmu3/mm] tw YZ)/(1+2 YH+YH^2)+(3 Log[YZ] Log[mmu3/mm] tw YZ^2)/(1+2 YH+YH^2)+(18 Log[YZ] Log[mmu3/mm] tw)/(1+2 YH+YH^2)-(160 Zeta[2])/(3 (1-YZ))+(32 Zeta[2])/((3 (1-YZ)) tw)+(200 Zeta[2] tw)/(3 (1-YZ))-(320 PolyLog[2,-YZ])/(3 (1-YZ))+(64 PolyLog[2,-YZ])/((3 (1-YZ)) tw)+(400 PolyLog[2,-YZ] tw)/(3 (1-YZ))-(80 Log[YZ] Log[YZ])/(3 (1-YZ))+(16 Log[YZ] Log[YZ])/((3 (1-YZ)) tw)+(100 Log[YZ] Log[YZ] tw)/(3 (1-YZ))+(256 Zeta[2])/((9 (1+YZ)) tw)-(256 Zeta[2] Log[1+YZ])/((9 (1+YZ)) tw)-(512 Zeta[2] Log[2])/((9 (1+YZ)) tw)+(128 Zeta[3])/((9 (1+YZ)) tw)-(832 PolyLog[2,-YZ])/((27 (1+YZ)) tw)-(512 PolyLog[2,-YZ] Log[YZ])/((27 (1+YZ)) tw)-(512 PolyLog[2,YZ])/((27 (1+YZ)) tw)-(1024 PolyLog[2,YZ] Log[YZ])/((27 (1+YZ)) tw)+(256 PolyLog[3,-YZ])/((9 (1+YZ)) tw)+(512 PolyLog[3,YZ])/((9 (1+YZ)) tw)+(352 Log[YZ])/((27 (1+YZ)) tw)-(512 Log[YZ] Log[1-YZ])/((27 (1+YZ)) tw)-(256 Log[YZ] Log[1+YZ])/((27 (1+YZ)) tw)+(32 Log[YZ] Log[mmu3/mm])/((9 (1+YZ)) tw)+(160 Log[YZ] Log[YZ])/((27 (1+YZ)) tw)-(256 Log[YZ] Log[YZ] Log[1-YZ])/((27 (1+YZ)) tw)-(128 Log[YZ] Log[YZ] Log[1+YZ])/((27 (1+YZ)) tw)-(224 Zeta[2])/((9 (1+2 YZ+YZ^2)) tw)+(256 Zeta[2] Log[1+YZ])/((9 (1+2 YZ+YZ^2)) tw)+(512 Zeta[2] Log[2])/((9 (1+2 YZ+YZ^2)) tw)-(128 Zeta[3])/((9 (1+2 YZ+YZ^2)) tw)+(512 PolyLog[2,-YZ] Log[YZ])/((27 (1+2 YZ+YZ^2)) tw)+(1024 PolyLog[2,YZ] Log[YZ])/((27 (1+2 YZ+YZ^2)) tw)-(256 PolyLog[3,-YZ])/((9 (1+2 YZ+YZ^2)) tw)-(512 PolyLog[3,YZ])/((9 (1+2 YZ+YZ^2)) tw)-(112 Log[YZ] Log[YZ])/((27 (1+2 YZ+YZ^2)) tw)+(256 Log[YZ] Log[YZ] Log[1-YZ])/((27 (1+2 YZ+YZ^2)) tw)+(128 Log[YZ] Log[YZ] Log[1+YZ])/((27 (1+2 YZ+YZ^2)) tw)+(470 Zeta[2])/9-(20 Zeta[2])/(3 tw^2)-(64 Zeta[2] YZ)/(9 tw)-(65 Zeta[2])/(3 tw)-(2 Zeta[2] tw)/YH-6 Zeta[2] tw YH-Zeta[2] tw YH^2-(34 Zeta[2] tw)/(9 YZ^2)-(133 Zeta[2] tw)/(9 YZ)-535/9 Zeta[2] tw YZ-211/9 Zeta[2] tw YZ^2-34/9 Zeta[2] tw YZ^3-739/9 Zeta[2] tw+(80 Zeta[2])/(9 YZ)+400/9 Zeta[2] YZ+80/9 Zeta[2] YZ^2+(20 Zeta[2] Log[1-1/tw])/(3 tw^2)-(10 Zeta[2] Log[1-1/tw])/tw+10/3 Zeta[2] Log[1-1/tw] tw+(2 Zeta[2] Log[1+YH] tw)/YH^2-(4 Zeta[2] Log[1+YH] tw)/YH-4 Zeta[2] Log[1+YH] tw YH+2 Zeta[2] Log[1+YH] tw YH^2+4 Zeta[2] Log[1+YH] tw-160/9 Zeta[2] Log[1+YZ]+(64 Zeta[2] Log[1+YZ])/(9 tw YZ)+(64 Zeta[2] Log[1+YZ] YZ)/(9 tw)+(128 Zeta[2] Log[1+YZ])/(9 tw)+(34 Zeta[2] Log[1+YZ] tw)/(9 YZ^3)+(50 Zeta[2] Log[1+YZ] tw)/(3 YZ^2)+(266 Zeta[2] Log[1+YZ] tw)/(9 YZ)+266/9 Zeta[2] Log[1+YZ] tw YZ+50/3 Zeta[2] Log[1+YZ] tw YZ^2+34/9 Zeta[2] Log[1+YZ] tw YZ^3+100/3 Zeta[2] Log[1+YZ] tw-(80 Zeta[2] Log[1+YZ])/(9 YZ^2)-(320 Zeta[2] Log[1+YZ])/(9 YZ)-320/9 Zeta[2] Log[1+YZ] YZ-80/9 Zeta[2] Log[1+YZ] YZ^2+512/9 Zeta[2] Log[2]-(128 Zeta[3])/9-(4 PolyLog[2,1-1/tw] Log[1-1/tw])/tw^2+(6 PolyLog[2,1-1/tw] Log[1-1/tw])/tw-2 PolyLog[2,1-1/tw] Log[1-1/tw] tw-2/3 PolyLog[2,1/tw]+(4 PolyLog[2,1/tw])/(3 tw^2)+(11 PolyLog[2,1/tw])/(3 tw)-3 PolyLog[2,1/tw] tw-(4 PolyLog[2,1/tw] Log[1-1/tw])/(3 tw^2)+(2 PolyLog[2,1/tw] Log[1-1/tw])/tw-2/3 PolyLog[2,1/tw] Log[1-1/tw] tw-(5 PolyLog[2,-YH] tw)/(3 YH^2)+(28 PolyLog[2,-YH] tw)/(3 YH)-28/3 PolyLog[2,-YH] tw YH+5/3 PolyLog[2,-YH] tw YH^2+(4 PolyLog[2,-YH] Log[YH] tw)/(3 YH^2)-(8 PolyLog[2,-YH] Log[YH] tw)/(3 YH)-8/3 PolyLog[2,-YH] Log[YH] tw YH+4/3 PolyLog[2,-YH] Log[YH] tw YH^2+8/3 PolyLog[2,-YH] Log[YH] tw+160/3 PolyLog[2,-YZ]-(64 PolyLog[2,-YZ])/(27 tw YZ)+(64 PolyLog[2,-YZ] YZ)/(27 tw)+(128 PolyLog[2,-YZ])/(27 tw)-(34 PolyLog[2,-YZ] tw)/(27 YZ^3)-(23 PolyLog[2,-YZ] tw)/(9 YZ^2)+(46 PolyLog[2,-YZ] tw)/(3 YZ)-46/3 PolyLog[2,-YZ] tw YZ+23/9 PolyLog[2,-YZ] tw YZ^2+34/27 PolyLog[2,-YZ] tw YZ^3-200/3 PolyLog[2,-YZ] tw+(80 PolyLog[2,-YZ])/(27 YZ^2)+(320 PolyLog[2,-YZ])/(27 YZ)-320/27 PolyLog[2,-YZ] YZ-80/27 PolyLog[2,-YZ] YZ^2-320/27 PolyLog[2,-YZ] Log[YZ]+(128 PolyLog[2,-YZ] Log[YZ])/(27 tw YZ)+(128 PolyLog[2,-YZ] Log[YZ] YZ)/(27 tw)+(256 PolyLog[2,-YZ] Log[YZ])/(27 tw)+(68 PolyLog[2,-YZ] Log[YZ] tw)/(27 YZ^3)+(100 PolyLog[2,-YZ] Log[YZ] tw)/(9 YZ^2)+(532 PolyLog[2,-YZ] Log[YZ] tw)/(27 YZ)+532/27 PolyLog[2,-YZ] Log[YZ] tw YZ+100/9 PolyLog[2,-YZ] Log[YZ] tw YZ^2+68/27 PolyLog[2,-YZ] Log[YZ] tw YZ^3+200/9 PolyLog[2,-YZ] Log[YZ] tw-(160 PolyLog[2,-YZ] Log[YZ])/(27 YZ^2)-(640 PolyLog[2,-YZ] Log[YZ])/(27 YZ)-640/27 PolyLog[2,-YZ] Log[YZ] YZ-160/27 PolyLog[2,-YZ] Log[YZ] YZ^2-(4 PolyLog[2,YH] tw)/(3 YH^2)+(8 PolyLog[2,YH] tw)/(3 YH)-8/3 PolyLog[2,YH] tw YH+4/3 PolyLog[2,YH] tw YH^2+(8 PolyLog[2,YH] Log[YH] tw)/(3 YH^2)-(16 PolyLog[2,YH] Log[YH] tw)/(3 YH)-16/3 PolyLog[2,YH] Log[YH] tw YH+8/3 PolyLog[2,YH] Log[YH] tw YH^2+16/3 PolyLog[2,YH] Log[YH] tw-(128 PolyLog[2,YZ])/(27 tw YZ)+(128 PolyLog[2,YZ] YZ)/(27 tw)+(256 PolyLog[2,YZ])/(27 tw)-(68 PolyLog[2,YZ] tw)/(27 YZ^3)-(100 PolyLog[2,YZ] tw)/(9 YZ^2)-(44 PolyLog[2,YZ] tw)/(3 YZ)+44/3 PolyLog[2,YZ] tw YZ+100/9 PolyLog[2,YZ] tw YZ^2+68/27 PolyLog[2,YZ] tw YZ^3+(160 PolyLog[2,YZ])/(27 YZ^2)+(640 PolyLog[2,YZ])/(27 YZ)-640/27 PolyLog[2,YZ] YZ-160/27 PolyLog[2,YZ] YZ^2-640/27 PolyLog[2,YZ] Log[YZ]+(256 PolyLog[2,YZ] Log[YZ])/(27 tw YZ)+(256 PolyLog[2,YZ] Log[YZ] YZ)/(27 tw)+(512 PolyLog[2,YZ] Log[YZ])/(27 tw)+(136 PolyLog[2,YZ] Log[YZ] tw)/(27 YZ^3)+(200 PolyLog[2,YZ] Log[YZ] tw)/(9 YZ^2)+(1064 PolyLog[2,YZ] Log[YZ] tw)/(27 YZ)+1064/27 PolyLog[2,YZ] Log[YZ] tw YZ+200/9 PolyLog[2,YZ] Log[YZ] tw YZ^2+136/27 PolyLog[2,YZ] Log[YZ] tw YZ^3+400/9 PolyLog[2,YZ] Log[YZ] tw-(320 PolyLog[2,YZ] Log[YZ])/(27 YZ^2)-(1280 PolyLog[2,YZ] Log[YZ])/(27 YZ)-1280/27 PolyLog[2,YZ] Log[YZ] YZ-320/27 PolyLog[2,YZ] Log[YZ] YZ^2+(4 PolyLog[3,1-1/tw])/tw^2-(6 PolyLog[3,1-1/tw])/tw+2 PolyLog[3,1-1/tw] tw-(2 PolyLog[3,-YH] tw)/YH^2+(4 PolyLog[3,-YH] tw)/YH+4 PolyLog[3,-YH] tw YH-2 PolyLog[3,-YH] tw YH^2-4 PolyLog[3,-YH] tw+160/9 PolyLog[3,-YZ]-(64 PolyLog[3,-YZ])/(9 tw YZ)-(64 PolyLog[3,-YZ] YZ)/(9 tw)-(128 PolyLog[3,-YZ])/(9 tw)-(34 PolyLog[3,-YZ] tw)/(9 YZ^3)-(50 PolyLog[3,-YZ] tw)/(3 YZ^2)-(266 PolyLog[3,-YZ] tw)/(9 YZ)-266/9 PolyLog[3,-YZ] tw YZ-50/3 PolyLog[3,-YZ] tw YZ^2-34/9 PolyLog[3,-YZ] tw YZ^3-100/3 PolyLog[3,-YZ] tw+(80 PolyLog[3,-YZ])/(9 YZ^2)+(320 PolyLog[3,-YZ])/(9 YZ)+320/9 PolyLog[3,-YZ] YZ+80/9 PolyLog[3,-YZ] YZ^2-(4 PolyLog[3,YH] tw)/YH^2+(8 PolyLog[3,YH] tw)/YH+8 PolyLog[3,YH] tw YH-4 PolyLog[3,YH] tw YH^2-8 PolyLog[3,YH] tw+320/9 PolyLog[3,YZ]-(128 PolyLog[3,YZ])/(9 tw YZ)-(128 PolyLog[3,YZ] YZ)/(9 tw)-(256 PolyLog[3,YZ])/(9 tw)-(68 PolyLog[3,YZ] tw)/(9 YZ^3)-(100 PolyLog[3,YZ] tw)/(3 YZ^2)-(532 PolyLog[3,YZ] tw)/(9 YZ)-532/9 PolyLog[3,YZ] tw YZ-100/3 PolyLog[3,YZ] tw YZ^2-68/9 PolyLog[3,YZ] tw YZ^3-200/3 PolyLog[3,YZ] tw+(160 PolyLog[3,YZ])/(9 YZ^2)+(640 PolyLog[3,YZ])/(9 YZ)+640/9 PolyLog[3,YZ] YZ+160/9 PolyLog[3,YZ] YZ^2-2/3 Log[1-1/tw]-(5 Log[1-1/tw])/(3 tw^2)+(7 Log[1-1/tw])/(2 tw)-7/6 Log[1-1/tw] tw-Log[1-1/tw] Log[1-1/tw]+(2 Log[1-1/tw] Log[1-1/tw])/(3 tw^2)-(Log[1-1/tw] Log[1-1/tw])/(2 tw)+5/6 Log[1-1/tw] Log[1-1/tw] tw+(11 Log[1+YH] tw)/(6 YH^2)-(14 Log[1+YH] tw)/(3 YH)-14/3 Log[1+YH] tw YH+11/6 Log[1+YH] tw YH^2-13 Log[1+YH] tw-680/9 Log[1+YZ]+(80 Log[1+YZ])/(27 tw YZ)+(80 Log[1+YZ] YZ)/(27 tw)+(736 Log[1+YZ])/(27 tw)+(85 Log[1+YZ] tw)/(54 YZ^3)+(275 Log[1+YZ] tw)/(18 YZ^2)+(845 Log[1+YZ] tw)/(18 YZ)+845/18 Log[1+YZ] tw YZ+275/18 Log[1+YZ] tw YZ^2+85/54 Log[1+YZ] tw YZ^3+1795/27 Log[1+YZ] tw-(100 Log[1+YZ])/(27 YZ^2)-(1120 Log[1+YZ])/(27 YZ)-1120/27 Log[1+YZ] YZ-100/27 Log[1+YZ] YZ^2-3 Log[1/tw]+(5 Log[1/tw])/(3 tw^2)+Log[1/tw]/(2 tw)+(3 Log[1/tw] Log[1-1/tw])/tw-3 Log[1/tw] Log[1-1/tw] tw-(2 Log[1/tw] Log[1-1/tw] Log[1-1/tw])/tw^2+(3 Log[1/tw] Log[1-1/tw] Log[1-1/tw])/tw-Log[1/tw] Log[1-1/tw] Log[1-1/tw] tw+(Log[1/tw] Log[mmu3/mm])/tw^2-(3 Log[1/tw] Log[mmu3/mm])/(2 tw)+73/18 Log[mmu3/mm]-(25 Log[mmu3/mm])/(9 tw)-(4 Log[mmu3/mm] tw)/YH-4 Log[mmu3/mm] tw YH-(17 Log[mmu3/mm] tw)/(18 YZ^2)-(151 Log[mmu3/mm] tw)/(18 YZ)-151/18 Log[mmu3/mm] tw YZ-17/18 Log[mmu3/mm] tw YZ^2-152/9 Log[mmu3/mm] tw+(20 Log[mmu3/mm])/(9 YZ)+20/9 Log[mmu3/mm] YZ-(Log[mmu3/mm] Log[1-1/tw])/tw^2+(3 Log[mmu3/mm] Log[1-1/tw])/(2 tw)-1/2 Log[mmu3/mm] Log[1-1/tw] tw+(Log[mmu3/mm] Log[1+YH] tw)/(2 YH^2)+(2 Log[mmu3/mm] Log[1+YH] tw)/YH+2 Log[mmu3/mm] Log[1+YH] tw YH+1/2 Log[mmu3/mm] Log[1+YH] tw YH^2+3 Log[mmu3/mm] Log[1+YH] tw-40/3 Log[mmu3/mm] Log[1+YZ]+(16 Log[mmu3/mm] Log[1+YZ])/(9 tw YZ)+(16 Log[mmu3/mm] Log[1+YZ] YZ)/(9 tw)+(32 Log[mmu3/mm] Log[1+YZ])/(9 tw)+(17 Log[mmu3/mm] Log[1+YZ] tw)/(18 YZ^3)+(25 Log[mmu3/mm] Log[1+YZ] tw)/(6 YZ^2)+(49 Log[mmu3/mm] Log[1+YZ] tw)/(6 YZ)+49/6 Log[mmu3/mm] Log[1+YZ] tw YZ+25/6 Log[mmu3/mm] Log[1+YZ] tw YZ^2+17/18 Log[mmu3/mm] Log[1+YZ] tw YZ^3+89/9 Log[mmu3/mm] Log[1+YZ] tw-(20 Log[mmu3/mm] Log[1+YZ])/(9 YZ^2)-(80 Log[mmu3/mm] Log[1+YZ])/(9 YZ)-80/9 Log[mmu3/mm] Log[1+YZ] YZ-20/9 Log[mmu3/mm] Log[1+YZ] YZ^2-4/3 Log[mmu3/mm] Log[mmu3/mm]+(3 Log[mmu3/mm] Log[mmu3/mm] tw)/(2 YH)+3/2 Log[mmu3/mm] Log[mmu3/mm] tw YH+(4 Log[mmu3/mm] Log[mmu3/mm] tw)/(3 YZ)+4/3 Log[mmu3/mm] Log[mmu3/mm] tw YZ+8/3 Log[mmu3/mm] Log[mmu3/mm] tw+14/3 Log[YH] tw YH-11/6 Log[YH] tw YH^2+13/2 Log[YH] tw-(4 Log[YH] Log[1-YH] tw)/(3 YH^2)+(8 Log[YH] Log[1-YH] tw)/(3 YH)-8/3 Log[YH] Log[1-YH] tw YH+4/3 Log[YH] Log[1-YH] tw YH^2-(2 Log[YH] Log[1+YH] tw)/(3 YH^2)+(4 Log[YH] Log[1+YH] tw)/(3 YH)-4/3 Log[YH] Log[1+YH] tw YH+2/3 Log[YH] Log[1+YH] tw YH^2-(3 Log[YH] Log[mmu3/mm] tw)/(2 YH)-1/2 Log[YH] Log[mmu3/mm] tw YH-1/2 Log[YH] Log[mmu3/mm] tw YH^2-3/2 Log[YH] Log[mmu3/mm] tw+(Log[YH] Log[YH] tw)/(3 YH)-5/3 Log[YH] Log[YH] tw YH-1/2 Log[YH] Log[YH] tw YH^2+4/3 Log[YH] Log[YH] tw+(2 Log[YH] Log[YH] Log[1-YH] tw)/(3 YH^2)-(4 Log[YH] Log[YH] Log[1-YH] tw)/(3 YH)-4/3 Log[YH] Log[YH] Log[1-YH] tw YH+2/3 Log[YH] Log[YH] Log[1-YH] tw YH^2+4/3 Log[YH] Log[YH] Log[1-YH] tw+(Log[YH] Log[YH] Log[1+YH] tw)/(3 YH^2)-(2 Log[YH] Log[YH] Log[1+YH] tw)/(3 YH)-2/3 Log[YH] Log[YH] Log[1+YH] tw YH+1/3 Log[YH] Log[YH] Log[1+YH] tw YH^2+2/3 Log[YH] Log[YH] Log[1+YH] tw+(340 Log[YZ])/9-(80 Log[YZ] YZ)/(27 tw)-(544 Log[YZ])/(27 tw)-(34 Log[YZ] tw)/(9 YZ^2)-(317 Log[YZ] tw)/(18 YZ)-88/3 Log[YZ] tw YZ-23/2 Log[YZ] tw YZ^2-85/54 Log[YZ] tw YZ^3-1795/54 Log[YZ] tw+(80 Log[YZ])/(9 YZ)+880/27 Log[YZ] YZ+100/27 Log[YZ] YZ^2-(128 Log[YZ] Log[1-YZ])/(27 tw YZ)+(128 Log[YZ] Log[1-YZ] YZ)/(27 tw)+(256 Log[YZ] Log[1-YZ])/(27 tw)-(68 Log[YZ] Log[1-YZ] tw)/(27 YZ^3)-(100 Log[YZ] Log[1-YZ] tw)/(9 YZ^2)-(44 Log[YZ] Log[1-YZ] tw)/(3 YZ)+44/3 Log[YZ] Log[1-YZ] tw YZ+100/9 Log[YZ] Log[1-YZ] tw YZ^2+68/27 Log[YZ] Log[1-YZ] tw YZ^3+(160 Log[YZ] Log[1-YZ])/(27 YZ^2)+(640 Log[YZ] Log[1-YZ])/(27 YZ)-640/27 Log[YZ] Log[1-YZ] YZ-160/27 Log[YZ] Log[1-YZ] YZ^2-(64 Log[YZ] Log[1+YZ])/(27 tw YZ)+(64 Log[YZ] Log[1+YZ] YZ)/(27 tw)+(128 Log[YZ] Log[1+YZ])/(27 tw)-(34 Log[YZ] Log[1+YZ] tw)/(27 YZ^3)-(50 Log[YZ] Log[1+YZ] tw)/(9 YZ^2)-(22 Log[YZ] Log[1+YZ] tw)/(3 YZ)+22/3 Log[YZ] Log[1+YZ] tw YZ+50/9 Log[YZ] Log[1+YZ] tw YZ^2+34/27 Log[YZ] Log[1+YZ] tw YZ^3+(80 Log[YZ] Log[1+YZ])/(27 YZ^2)+(320 Log[YZ] Log[1+YZ])/(27 YZ)-320/27 Log[YZ] Log[1+YZ] YZ-80/27 Log[YZ] Log[1+YZ] YZ^2+20/3 Log[YZ] Log[mmu3/mm]-(16 Log[YZ] Log[mmu3/mm] YZ)/(9 tw)-(32 Log[YZ] Log[mmu3/mm])/(9 tw)-(4 Log[YZ] Log[mmu3/mm] tw)/(3 YZ)-41/6 Log[YZ] Log[mmu3/mm] tw YZ-25/6 Log[YZ] Log[mmu3/mm] tw YZ^2-17/18 Log[YZ] Log[mmu3/mm] tw YZ^3-89/18 Log[YZ] Log[mmu3/mm] tw+80/9 Log[YZ] Log[mmu3/mm] YZ+20/9 Log[YZ] Log[mmu3/mm] YZ^2+500/27 Log[YZ] Log[YZ]-(32 Log[YZ] Log[YZ] YZ)/(9 tw)-(160 Log[YZ] Log[YZ])/(27 tw)+(17 Log[YZ] Log[YZ] tw)/(27 YZ^2)+(67 Log[YZ] Log[YZ] tw)/(18 YZ)-335/18 Log[YZ] Log[YZ] tw YZ-497/54 Log[YZ] Log[YZ] tw YZ^2-17/9 Log[YZ] Log[YZ] tw YZ^3-685/27 Log[YZ] Log[YZ] tw-(40 Log[YZ] Log[YZ])/(27 YZ)+440/27 Log[YZ] Log[YZ] YZ+40/9 Log[YZ] Log[YZ] YZ^2-160/27 Log[YZ] Log[YZ] Log[1-YZ]+(64 Log[YZ] Log[YZ] Log[1-YZ])/(27 tw YZ)+(64 Log[YZ] Log[YZ] Log[1-YZ] YZ)/(27 tw)+(128 Log[YZ] Log[YZ] Log[1-YZ])/(27 tw)+(34 Log[YZ] Log[YZ] Log[1-YZ] tw)/(27 YZ^3)+(50 Log[YZ] Log[YZ] Log[1-YZ] tw)/(9 YZ^2)+1/(27 YZ) 266 Log[YZ] Log[YZ] Log[1-YZ] tw+266/27 Log[YZ] Log[YZ] Log[1-YZ] tw YZ+50/9 Log[YZ] Log[YZ] Log[1-YZ] tw YZ^2+34/27 Log[YZ] Log[YZ] Log[1-YZ] tw YZ^3+100/9 Log[YZ] Log[YZ] Log[1-YZ] tw-(80 Log[YZ] Log[YZ] Log[1-YZ])/(27 YZ^2)-(320 Log[YZ] Log[YZ] Log[1-YZ])/(27 YZ)-320/27 Log[YZ] Log[YZ] Log[1-YZ] YZ-80/27 Log[YZ] Log[YZ] Log[1-YZ] YZ^2-80/27 Log[YZ] Log[YZ] Log[1+YZ]+(32 Log[YZ] Log[YZ] Log[1+YZ])/(27 tw YZ)+(32 Log[YZ] Log[YZ] Log[1+YZ] YZ)/(27 tw)+(64 Log[YZ] Log[YZ] Log[1+YZ])/(27 tw)+(17 Log[YZ] Log[YZ] Log[1+YZ] tw)/(27 YZ^3)+(25 Log[YZ] Log[YZ] Log[1+YZ] tw)/(9 YZ^2)+1/(27 YZ) 133 Log[YZ] Log[YZ] Log[1+YZ] tw+133/27 Log[YZ] Log[YZ] Log[1+YZ] tw YZ+25/9 Log[YZ] Log[YZ] Log[1+YZ] tw YZ^2+17/27 Log[YZ] Log[YZ] Log[1+YZ] tw YZ^3+50/9 Log[YZ] Log[YZ] Log[1+YZ] tw-(40 Log[YZ] Log[YZ] Log[1+YZ])/(27 YZ^2)-(160 Log[YZ] Log[YZ] Log[1+YZ])/(27 YZ)-160/27 Log[YZ] Log[YZ] Log[1+YZ] YZ-40/27 Log[YZ] Log[YZ] Log[1+YZ] YZ^2)]


sigmaaS[alphaS_]=With[{Cf=4/3},-Cf alphaS/\[Pi]];
sigmaaS[mt_,alphaS_,mu_]=With[{Cf=4/3,z11aS=-3*4/3},-alphaS/(4\[Pi]) (4Cf+2z11aS Log[mt/mu])]


deltaytaS[aS_]=sigmaaS[aS];
deltaytaS[mt_,aS_,mt_]=sigmaaS[aS];
deltaytaS[mt_,aS_,mu_]=sigmaaS[mt,aS,mu];


deltaytaSaS[aS_]=With[{Nf=5},+(1.0414Nf-14.3323) (aS/\[Pi])^2];


deltaytaSaS[mt_,aS_,mt_]:=deltaytaSaS[aS]
deltaytaSaS[mt_,aS_,mu_]:=With[{c1=-8,c2=-108,b3=-(11-2/3 6(*Nf*)),t=Log[mu/mt]},
deltaytaSaS[aS]+(aS^2 t (c2+b3 c1 t))/(16 \[Pi]^2)]


deltaytaSaSaS[aS_]=With[{Nf=5},(-198.7068+26.9239Nf-0.65269Nf^2)(aS/\[Pi])^3];


deltaytaSaSaS[mt_,aS_,mt_]:=deltaytaSaSaS[aS]
deltaytaSaSaS[mt_,aS_,mu_]:=With[{c1=-8,c2=-108,c3=2*(-(2083/3)+320 Zeta[3]),b3=-(11-2/3 6(*Nf*)),B33=-2(51-19/3 6(*Nf*)),t=Log[mu/mt]},
deltaytaSaSaS[aS]+(aS^3 t (3 c3+t (3 B33 c1+6 b3 c2+4 b3^2 c1 t)))/(192 \[Pi]^3)]


deltayta[mH_,mt_,a_,mu_]:=Re[sigmaa[mH,mt,a,mu]]+deltaMSGFa[mH,mt,a,mu]/2


deltaytaaS[mH_,mt_,a_,aS_,mu_]:=Re[(sigmaaaS[mH,mt,a,aS,mu]+deltaMSGFaaS[mH,mt,a,aS,mu]/2)+1/2 sigmaaS[mt,aS,mu]deltaMSGFa[mH,mt,a,mu]]


constantsTree[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],yt0->Sqrt[2^(3/2)gF]Mt,lambda0->Mh^2 gF/Sqrt[2],mu0->mu}]


constantsQCD1[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF]Mt( 1+deltaytaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]),
mu0->mu}]]


constantsQCD2[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF]Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]),
mu0->mu}]]


constantsQCD3[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF]Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltaytaSaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]),
mu0->mu}]]


constantsQCD3top2[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],aSmu=alphaS5[aSMZ,mu],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF]Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltaytaSaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]+deltaytaaS[Mh,Mt,alpha,aSmu,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]),
mu0->mu}]]


constantsQCD3top2higgs2[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],aSmu=alphaS5[aSMZ,mu],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF] Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltaytaSaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]+deltaytaaS[Mh,Mt,alpha,aSmu,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]+deltahaaS[Mh,Mt,aSmu,alpha,mu]),
mu0->mu}]]


constantsQCD3top2higgs3[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],aSmu=alphaS5[aSMZ,mu],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF] Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltaytaSaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]+deltaytaaS[Mh,Mt,alpha,aSmu,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]+deltahaaS[Mh,Mt,aSmu,alpha,mu]+Re[deltahy6[Mh,Mt,mu]]),
mu0->mu}]]


constantsQCD3higgs2[Mh_?NumericQ,Mt_?NumericQ,aSMZ_?NumericQ,mu_?NumericQ]:=With[{aSMt=alphaS5[aSMZ,Mt],aSmu=alphaS5[aSMZ,mu],alpha=alpha[mu]},
N[{g10->gprime1loop[mu],g20->g1loop[mu],g30->gsQCD[Mt,aSMZ,mu],
yt0->Sqrt[2^(3/2)gF] Mt( 1+deltaytaS[Mt,aSMt,mu]+deltaytaSaS[Mt,aSMt,mu]+deltaytaSaSaS[Mt,aSMt,mu]+deltayta[Mh,Mt,alpha,mu]),
lambda0->Mh^2 gF/Sqrt[2](1+deltaha[Mh,Mt,alpha,mu]+deltahaaS[Mh,Mt,alpha,aSmu,mu]),
mu0->mu}]]


constantsQCD3top2higgs3Linold[mh_?NumericQ,mt_?NumericQ,as_?NumericQ,mt_?NumericQ]:=
N[{g10->0.3587322994941791` +0.000010380608695434968` (-192.44444444444443`+ 1.1111111111111112` mt),
g20->0.6483726244241163` -0.00002840241125869606` (-192.44444444444443`+ 1.1111111111111112` mt),
g30->1.1644608940056973` +0.0031229710943696948` (-169.14285714285717`+ 1428.5714285714287` as)-0.00041622386051933126` (-192.44444444444443`+ 1.1111111111111112` mt),
yt0->Sqrt[2^(3/2)gF] mt( 1+-0.058926400599624416`- 0.0004159558782009482` (-169.14285714285717`+ 1428.5714285714287` as)-0.000022208044265021815` (-126+mh)+9.57215582955301`*^-8 (-126+mh)^2+0.00011067901271296329` (-192.44444444444443`+ 1.1111111111111112` mt)),
lambda0->mh^2 gF/Sqrt[2](1+-0.024983909218006556`- 0.000056963752443996545` (-169.14285714285717`+ 1428.5714285714287` as)+0.000251373406983096` (-126+mh)-1.2657611254643557`*^-6 (-126+mh)^2-0.0003180731979862109` (-192.44444444444443`+ 1.1111111111111112` mt)-2.4123897736092518`*^-6 (-192.44444444444443`+ 1.1111111111111112` mt)^2),
mu0->mt}]


constantsQCD3top2higgs3Lin[mh_?NumericQ,mt_?NumericQ,as_?NumericQ,mt_?NumericQ]:=
N[{g10->0.3587323039141973` +0.00001038059502860946` (-192.44444444444443`+ 1.1111111111111112` mt),
g20->0.6483726118139727` -0.000028402371437823194` (-192.44444444444443`+ 1.1111111111111112` mt),
g30->1.1644606754702975` +0.0031229690634674997` (-169.14285714285717`+ 1428.5714285714287` as)-0.0004162230979694716` (-192.44444444444443`+ 1.1111111111111112` mt),
yt0->0.9361978958108839` -0.00041377722142376457` (-169.14285714285717`+ 1428.5714285714287` as)-0.000022176189843775126` (-125.5`+mh)+0.00497469373273379` (-192.44444444444443`+ 1.1111111111111112` mt),
lambda0->0.12663789253540672` +0.0020508236706197123` (-125.5`+mh)+8.399919821812363`*^-6 (-125.5`+mh)^2-0.000040953874289955` (-192.44444444444443`+ 1.1111111111111112` mt),
mu0->mt}]


End[] (* Private *)


On[General::spell1];


EndPackage[] (* SMPoleMatching *)