SpaceMath version 1.0:
 A Mathematica package for Beyond the Standard Model parameter space searches

Developers: 	M. A. Arroyo Ureña
			T. A. Valencia Pérez

Collaborators:	  M. Mondragón Ceballos, R. Gaitán
				
                                           & CIIEC

Content

Brief review

Introduction

Installation

First steps

Validation

Conclusion and perspectives

Installation

Automatic Installation:

Import["https://raw.githubusercontent.com/spacemathapp/spacemath/beta/SpaceMath/Install.m"]

InstallSpaceMath[]

Manual installation:

Download (https://github.com/spacemathapp/spacemath/archive/refs/heads/beta.zip)

Unzip the folder inside $UserBaseDirectory/Applications

$UserBaseDirectory

Update data & Delete package:

Update data:

UpdateSpaceMathData[]

Delete package:

DeleteSpaceMath[]

First steps

1&2.  Open a notebook and load SpaceMath v1.0

<<SpaceMath`

3.   Define couplings. For the THDM-III case they are given in Table

(*THDM-III couplings taken from arXiv:hep-ph/0509353v2*)

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))
ghtautau[a_,Atata_,Cab_,tb_]:=(g/2) (mtau/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mtau)*(mtau/vev*Atata)))
ghWW[sab_]:=gw*mW*sab
ghZZ[sab_]:=gz*mZ*sab

Signal Strength (Subscript[R, τ]).

?Rtau

Rtau[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],ghtautau[ArcCos[cab]+ArcTan[tb],1,cab,tb],
cab,tb,-1,1,1,15,"cos(α-β)","tanβ",Att,Abb,0.9,1,0.05,0.9,1,0.05,30][[2]]

?TableRtau

TableRtau[ghtt[ArcCos[cab]+ArcTan[tb],1,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],1,cab,tb],ghtautau[ArcCos[cab]+ArcTan[tb],1,cab,tb],cab,-1,1,0.1,tb,1,50,1]

SpaceMath-Signal Strengths-Random RW
Load SpaceMath

<<SpaceMath`

Enter couplings
(*THDM-III Couplings*)

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))
ghWW[sab_]:=gw*mW*sab

Evaluates RW

?RWRandom

RWRandom[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],ghWW[Sqrt[1-cab^2]],cab,-1,1,tb,0.1,20,Att,0.999,1,Abb,0.999,1,5000];

(*PLOT*)
?PlotRWRandom

PlotRWRandom[1,2,"cos(α-β)","tanβ"][[2]]

SpaceMath-Signal Strengths-Random RZ
Load SpaceMath

<<SpaceMath`

Enter couplings
(*THDM-III Couplings*)

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))
ghZZ[sab_]:=gz*mZ*sab

Evaluates RZ

?RZRandom

RZRandom[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],ghZZ[Sqrt[1-cab^2]],cab,-1,1,tb,0.1,20,Att,0.999,1,Abb,0.999,1,5000];

(*PLOT*)

?PlotRZRandom

PlotRZRandom[1,2,"cos(α-β)","tanβ"][[1]]

SpaceMath-Signal Strengths-Random (Subscript[R, b])

Load SpaceMath

<<SpaceMath`

Enter couplings

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))

Evaluates (Subscript[R, b])

?RbRandom

RbRandom[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],cab,-1,1,tb,0.1,20,Att,0.999,1,Abb,0.999,1,5000];

(*PLOT*)
?PlotRbRandom

PlotRbRandom[1,2,"cos(α-β)","tanβ"][[2]]

SpaceMath-Signal Strengths-Random (Subscript[R, τ])

Load SpaceMath

<<SpaceMath`

Enter couplings

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))
ghtautau[a_,Atata_,Cab_,tb_]:=(g/2) (mtau/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mtau)*(mtau/vev*Atata)))

Evaluates (Subscript[R, τ])

?RtauRandom

RtauRandom[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],ghtautau[ArcCos[cab]+ArcTan[tb],1,cab,tb],cab,-1,1,tb,0.1,20,Att,0.999,1,Abb,0.999,1,5000];

(*PLOT*)
?PlotRtauRandom

PlotRtauRandom[1,2,"cos(α-β)","tanβ"][[2]]

SpaceMath-Signal Strengths-Random (Subscript[R, γ])

Load SpaceMath

<<SpaceMath`

Enter couplings

ghtt[a_,Att_,Cab_,tb_]:=(g/2) (mt/mW) ((Cos[a]/(tb*Cos[ArcTan[tb]]))-(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev*Att)))
ghbb[a_,Abb_,Cab_,tb_]:=(g/2) (mb/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev*Abb)))
ghtautau[a_,Atata_,Cab_,tb_]:=(g/2) (mtau/mW) (((-Sin[a]*tb)/Sin[ArcTan[tb]])+(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mtau)*(mtau/vev*Atata)))
ghWW[sab_]:=gw*mW*sab

Evaluates (Subscript[R, γ])

?RgamRandom

RgamRandom[ghtt[ArcCos[cab]+ArcTan[tb],Att,cab,tb],ghbb[ArcCos[cab]+ArcTan[tb],Abb,cab,tb],ghWW[Sqrt[1-cab^2]],0,mCH,cab,-1,1,tb,0.1,20,Att,0.999,1,Abb,0.999,1,5000];

(*PLOT*)
?PlotRgamRandom

PlotRgamRandom[1,2,"cos(α-β)","tanβ"][[2]]

<<SpaceMath`

ghtt[α_, Att_,Cab_,tb_]:=g/2 (mt/mW)((-Cos[α]/tb*Cos[ArcTan[tb]]) +(Sqrt[2] Cab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev)*Att))
ghbb[α_, Abb_,Cab_,tb_]:= g/2 (mb/mW)((-Sin[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mb)*(mb/vev)*Abb))
ghmumu[α_, Amumu_,Cab_,tb_]:= g/2 (mmu/mW)((-Sin[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mmu)*(mmu/vev)*Amumu))
gHmumu[α_, Amumu_,sab_,tb_]:= g/2 (mmu/mW)((Cos[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (sab*tb)/(g*Sin[ArcTan[tb]]) (mW/mmu)*(mmu/vev)*Amumu))
ghtautau[α_, Atautau_,Cab_,tb_]:= g/2 (mtau/mW)((-Sin[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mmu)*(mtau/vev)*Atautau))
ghtaumu[Ataumu_,Cab_,tb_]:=((Cab*tb)/(Sqrt[2]*Sin[ArcTan[tb]]))*((Sqrt[mmu*mtau]/vev)*Ataumu)
gHtautau[α_, Atautau_,sab_,tb_]:= g/2 (mtau/mW)((Cos[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (sab*tb)/(g*Sin[ArcTan[tb]]) (mW/mtau)*(mtau/vev)*Atautau))
gHtt[α_, Att_,sab_,tb_]:=g/2 (mt/mW)((Sin[α]/tb*Cos[ArcTan[tb]]) +(Sqrt[2] sab/(g*tb*Cos[ArcTan[tb]]) (mW/mt)*(mt/vev)*Att))
gHtaumu[Ataumu_,sab_,tb_]:=((sab*tb)/(Sqrt[2]*Sin[ArcTan[tb]]))*((Sqrt[mmu*mtau]/vev)*Ataumu)
ghtautau[α_, Atata_,Cab_,tb_] := g/2 (mtau/mW)((-Sin[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/mtau)*(mtau/vev)*Atata))
gAmumu[tb_,Amumu_]:=((I*g/2) (mmu/mW))*(-tb+((Sqrt[2]*tb)/(g*Sin[ArcTan[tb]])*(mW/mmu)*((mmu*Amumu)/vev)))
gAtaumu[tb_,Ataumu_]:=I*(tb/(Sqrt[2]*Sin[ArcTan[tb]])*((mmu*Ataumu)/vev))
gAtautau[tb_,Atata_]:=((I*g/2) (mtau/mW))*(-tb+((Sqrt[2]*tb)/(g*Sin[ArcTan[tb]])*(mW/mtau)*((mtau*Atata)/vev)))
gAtt[tb_,Att_]:=((I*g/2)(mt/mW))*(-tb+((Sqrt[2]*tb)/(g*Sin[ArcTan[tb]])*(mW/mt)*((mtau*Att)/vev)))
ghWW[sab_]:= g*mW*sab
ghZZ[sab_] := g*mZ*sab
ghee[α_, Aee_,Cab_,tb_]:= g/2 (me/mW)((-Sin[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (Cab*tb)/(g*Sin[ArcTan[tb]]) (mW/me)*(me/vev)*Aee))
ghmue[Amue_,Cab_,tb_]:=((Cab*tb)/(Sqrt[2]*Sin[ArcTan[tb]]))*((Sqrt[mmu*me]/vev)*Amue)
gHmue[Amue_,sab_,tb_]:=((sab*tb)/(Sqrt[2]*Sin[ArcTan[tb]]))*((Sqrt[mmu*me]/vev)*Amue)
gHee[α_, Aee_,sab_,tb_]:= g/2 (me/mW)((Cos[α]*tb/Sin[ArcTan[tb]]) +(Sqrt[2] (sab*tb)/(g*Sin[ArcTan[tb]]) (mW/me)*(me/vev)*Aee))
gAmue[tb_,Amue_]:=I*(tb/(Sqrt[2]*Sin[ArcTan[tb]])*((mmu*Amue)/vev))
gAee[tb_,Aee_]:=((I*g/2) (me/mW))*(-tb+((Sqrt[2]*tb)/(g*Sin[ArcTan[tb]])*(mW/me)*((me*Aee)/vev)))

?muonAMDM

muonAMDM[ghmumu[ArcCos[Cab]+ArcTan[tb], 1,Cab,tb],ghtaumu[Ataumu,Cab,tb],gHmumu[ArcCos[Cab]+ArcTan[tb], 1,(Sqrt[1-Cab^2]),tb],gHtaumu[Ataumu,(Sqrt[1-Cab^2]),tb],gAmumu[tb,1],gAtaumu[tb,Ataumu],mH,1000, Cab, -1, 1,
tb, 0.1,50, Ataumu,0.85,1.1,mH, 500,1000,10000]

?PlotMuonAMDM

PlotMuonAMDM[1,2, "Cab", "tb"]

?Tau3Mu

Tau3Mu[ghmumu[ArcCos[Cab]+ArcTan[tb], 1,Cab,tb],ghtaumu[Ataumu,Cab,tb],gHmumu[ArcCos[Cab]+ArcTan[tb], 1,(Sqrt[1-Cab^2]),tb],gHtaumu[Ataumu,(Sqrt[1-Cab^2]),tb],gAmumu[tb,1],gAtaumu[tb,Ataumu],mH,1000, Cab, -1, 1,tb, 0.1,50, Ataumu,0.85,1.1,mH, 500,1000,10000]

PlotTau3Mu[1, 2, "Cab", "tb"]

?Mu3e

Mu3e[ghee[ArcCos[Cab]+ArcTan[tb], 1,Cab,tb],ghmue[1,Cab,tb],gHee[ArcCos[Cab]+ArcTan[tb], 1,(Sqrt[1-Cab^2]),tb],gHmue[1,(Sqrt[1-Cab^2]),tb],gAee[tb,1],gAmue[tb,1],mH,mA,Cab,-1,1,tb,0.1,50,mH,200,1000,mA,200,1000,5000]

PlotMu3e[1, 2, "Cab", "tb"]