Examples of usage of the Standard Model pole matching and running packages

Initialization

With[{dir=If[DirectoryName[$InputFileName]≠"",DirectoryName[$InputFileName],
NotebookDirectory[]]},
If[FreeQ[$Path,dir],AppendTo[$Path,dir]]]

<<"SMPoleMatching`"

<<"SMrunning`"

Pole matching

mt0=172.9;
aS0=0.1184;
mh0=130;

crule=constantsQCD3top2higgs2[mh0,mt0,aS0,mt0]

lambda0/.crule

yt0/.crule

Renormalization group

sol3=solveSMRG[beta3loop,constantsQCD3top2higgs2[mh0,mt0,aS0,mt0]]

sol2=solveSMRG[beta2loop,constantsQCD3top2higgs2[mh0,mt0,aS0,mt0]]

sol1=solveSMRG[beta1loop,constantsQCD3top2higgs2[mh0,mt0,aS0,mt0]]

LogLinearPlot[{λ[Log[mu/mu0]]/.sol1,λ[Log[mu/mu0]]/.sol2,λ[Log[mu/mu0]]/.sol3},{mu,200,1000mP},AxesOrigin->{Automatic,0}]

Reference Higgs mass

referencemH[beta3loop,constantsQCD3top2higgs2[#,mt0,aS0,mt0]&]
muOfLambdaMin[beta3loop,constantsQCD3top2higgs2[#,mt0,aS0,mt0]&,%]/mP

Nice Plots

{dmttouch,daStouch}={171.3-172.9,0.1186-0.1184}

The values for the Higgs and top quark mass errors are not up to date

Module[{mh=126,dh=1.2,dh2=2.2,daS=0.0007,dmt=1.1},
LogLinearPlot[Evaluate[{λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh,mt0,aS0,mt0]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh,mt0+dmt,aS0,mt0+dmt]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh,mt0-dmt,aS0,mt0-dmt]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh,mt0,aS0+daS,mt0]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh,mt0,aS0-daS,mt0]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh-dh,mt0-dmttouch,aS0-daStouch,mt0-dmttouch]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh+dh,mt0+dmttouch,aS0+daStouch,mt0+dmttouch]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh-dh2,mt0-dmttouch,aS0-daStouch,mt0-dmttouch]],
λ[Log[(μ/mu0)]]/.solveSMRG[beta3loop,constantsQCD3top2higgs2[mh+dh2,mt0+dmttouch,aS0+daStouch,mt0+dmttouch]]}],
{μ,200,10^20},
AxesOrigin->{Automatic,0},
PlotRange->{-0.03,0.06},
Frame->True,
FrameLabel->{"Scale μ, GeV","λ"},
Filling->{6->{{7},LightYellow},6->{{8},LightPink},7->{{9},LightPink}},
PlotStyle->{Blue,{Blue,Dashed},{Blue,Dashed},{Blue,Dotted},{Blue,Dotted},
Thickness[0.00001],Thickness[0.00001],Thickness[0.00001],Thickness[0.00001]},
PlotLabel->"Higgs mass (Subscript[M, h])="<>ToString[mh]<>" GeV"]]

referenceaS[bfuncs_,icondsmt_]:=
Module[{as},as/.FindRoot[lambdaMin[bfuncs,icondsmt[as]],{as,0.115,0.120}]]

Clear[ras1]
ras1[mh_?NumericQ,mt_?NumericQ]:=ras1[mh,mt]=referenceaS[beta3loop,constantsQCD3top2higgs2[mh,mt,#,mt]&]

cf2d68=PDF[BinormalDistribution[0],{ val/.FindRoot[NProbability[Sqrt[x^2+y^2]<val,{x,y}\[Distributed]BinormalDistribution[0]]*100==68.3,{val,1}],0}]
cf2d95=PDF[BinormalDistribution[0],{ val/.FindRoot[NProbability[Sqrt[x^2+y^2]<val,{x,y}\[Distributed]BinormalDistribution[0]]*100==95,{val,1}],0}]
cf2d99=PDF[BinormalDistribution[0],{ val/.FindRoot[NProbability[Sqrt[x^2+y^2]<val,{x,y}\[Distributed]BinormalDistribution[0]]*100==99,{val,1}],0}]

Module[{p1,p2,p,mh0=126,mt=172.9,dmt=1.1,as=0.1184,das=0.0007,dmh1=1.2,dmh2=2.2},
p1=Plot[{ras1[mh0,mt],ras1[mh0+dmh1,mt],ras1[mh0-dmh1,mt],ras1[mh0+dmh2,mt],ras1[mh0-dmh2,mt]},
{mt,170,176},
PlotRange->{0.116,0.121},
PlotPoints->3,
PlotStyle->({{Thick,c},{Dashed,c},{Dashed,c},{Dotted,c},{Dotted,c}}/.{c->Blue})];
p2=ContourPlot[PDF[BinormalDistribution[{mt,as},{dmt,das},0],{x,y}],
{x,170,176},{y,0.116,0.121},
Contours->{cf2d68,cf2d95}/dmt/das,
ColorFunction->(ColorData["BeachColors"][1-0.6(#)]&),
FrameLabel->{"Pole top mass (Subscript[M, t]), GeV","Strong coupling (Subscript[α, S])((Subscript[M, Z]))"}
];
Print[p=Show[p2,p1,PlotLabel->"Higgs mass (Subscript[M, h])="<>ToString[mh0]<>" GeV"]]]