Tutorial for multiloop calculations - Example Notebook

Example: gg->h fusion via light quarks hard matching coefficient at 2-loop level
Disclaimer: end result is not correct, didn’t check factors of 2, symmetry factors etc.

Initialising FeynCalc & FeynArts

Quit[]

$LoadAddOns={"FeynArts"};

<<FeynCalc`

$FAVerbose=0;

MTDperp[μ_,ν_]:=(MTD[μ,ν]-(1/(Pair[Momentum[n,D],Momentum[nb,D]]))(FVD[n,μ]FVD[nb,ν]+FVD[nb,μ]FVD[n,ν])).SUNDelta[a,b];

MTDperp2[μ_,ν_]:=(MTD[μ,ν]-(1/(Pair[Momentum[n,D],Momentum[nb,D]]))(FVD[n,μ]FVD[nb,ν]+FVD[nb,μ]FVD[n,ν]));

Diagram Generation

diags1=InsertFields[CreateTopologies[1,1->2,ExcludeTopologies->Reducible],{S[1]}->{V[5],V[5]},InsertionLevel->{Classes},Model->"SMQCD",ExcludeParticles->{U[1|2|3|4],F[1|2|4],V[1|2|3|4]}];

Paint[diags1,ColumnsXRows->{2,1}]

diags2=InsertFields[CreateTopologies[2,1->2,ExcludeTopologies->Reducible],{S[1]}->{V[5],V[5]},InsertionLevel->{Classes},Model->"SMQCD",ExcludeParticles->{U[1|2|3|4],F[1|2|4],V[1|2|3|4],S[1|2],F[3,{1}],F[3,{2}]}];

Paint[diags2,ColumnsXRows->{7,3}]

amp1L=FCFAConvert[CreateFeynAmp[diags1,Truncated->True,PreFactor->-1],IncomingMomenta->{p1+p2},OutgoingMomenta->{p1,p2},LoopMomenta->{k,l},DropSumOver->True,ChangeDimension->D,UndoChiralSplittings->True,LorentzIndexNames->{μ,ν,α,β,φ,ζ}]/.{MQU[_]->m,FCGV["EL"]->e}//Contract//FCGVToSymbol//SUNSimplify;amp1L/.MW->(1/SW)

amp2L=FCFAConvert[CreateFeynAmp[diags2,Truncated->True,PreFactor->-1],IncomingMomenta->{p1+p2},OutgoingMomenta->{p1,p2},LoopMomenta->{k,l},DropSumOver->True,ChangeDimension->D,UndoChiralSplittings->True,LorentzIndexNames->{μ,ν,α,β,φ,ζ}]/.{MQU[_]->m,FCGV["EL"]->e}//Contract//FCGVToSymbol//SUNSimplify;amp2L/.MW->(1/SW)

1-Loop Result

Reduction to scalar integrals

Factor 2 because of two directions of fermion line

num=2TR[GAD[μ].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[ν].(GSD[k]+m)].((MTDperp2[μ,ν])/(D-2))//Contract;

We only need the leading (Subscript[m, b]) term, all other terms are power suppressed

num=Coefficient[num,m]*m//Simplify;

Express everything in terms of propagators: (k^2)=(Subscript[D, 1]), (((k+(Subscript[p, 1])))^2)=(Subscript[D, 2]), (((k-(Subscript[p, 2])))^2)=(Subscript[D, 3])

num=num/.{Pair[Momentum[n,D],Momentum[n,D]]->0,Pair[Momentum[n,D],Momentum[nb,D]]->2,Pair[Momentum[nb,D],Momentum[nb,D]]->0,Pair[Momentum[p1,D],Momentum[p1,D]]->0,Pair[Momentum[p2,D],Momentum[p2,D]]->0,Pair[Momentum[p1,D],Momentum[p2,D]]->((MH^2)/2),Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[nb,D],Momentum[p1,D]]->MH,Pair[Momentum[n,D],Momentum[p2,D]]->MH,Pair[Momentum[nb,D],Momentum[p2,D]]->0,Pair[Momentum[k,D],Momentum[k,D]]->D1,Pair[Momentum[k,D],Momentum[p1,D]]->(1/2)(D2-D1),Pair[Momentum[k,D],Momentum[p2,D]]->((-1)/2)(D3-D1),Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[n,D],Momentum[k,D]]->(1/MH)(D2-D1),Pair[Momentum[nb,D],Momentum[k,D]]->((-1)/MH)(D3-D1)};

tmp=(num/(D1 D2 D3));

Now decompose the full expression into scalar integrals of the form I(a,b,c)=∫dk ((Subscript[D, 1])^(-a))((Subscript[D, 2])^(-b))((Subscript[D, 3])^(-c))

tmp=tmp//Expand;
Do[exp1[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D1]],{i1,1,Length[tmp]}]
Do[exp2[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D2]],{i1,1,Length[tmp]}]
Do[exp3[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D3]],{i1,1,Length[tmp]}]
listA=List[];
Do[listA=Append[listA,j[RA,-exp1[i1],-exp2[i1],-exp3[i1]]],{i1,1,Length[tmp]}]
coefA=List[];
Do[coefA=Append[coefA,tmp[[i1]]*(D1^(-exp1[i1]))*(D2^(-exp2[i1]))*(D3^(-exp3[i1]))],{i1,1,Length[tmp]}]

listA//StandardForm
listA//Variables//StandardForm

coefA//StandardForm

Quit

Computation of Master Integrals

<<X`

LoopIntegrate[k.k,k,{k+p1,0},{k-p2,0}]/.{p1.p1->0,p2.p2->0,p1.p2->((MH^2)/2)}//LoopRefine//StandardForm

LoopIntegrate[1,k,{k+p1,0},{k-p2,0}]/.{p1.p1->0,p2.p2->0,p1.p2->((MH^2)/2)}//LoopRefine//StandardForm

LoopIntegrate[1,k,{k,0},{k+p1,0},{k-p2,0}]/.{p1.p1->0,p2.p2->0,p1.p2->((MH^2)/2)}//LoopRefine//StandardForm

reps={D->4-2ϵ,j[RA,-1,1,1]->-(MH^2)-(1/2) (MH^2) ((1/ϵ)+Log[-((µ^2)/(MH^2))]),j[RA,0,0,1]->0,j[RA,0,1,0]->0,j[RA,1,0,0]->0,j[RA,0,1,1]->2+(1/ϵ)+Log[-((µ^2)/(MH^2))],j[RA,1,1,1]->-((π^2)/(12 (MH^2)))+(((1/(ϵ^2))+((Log[-((µ^2)/(MH^2))])/ϵ)+(1/2) ((Log[-((µ^2)/(MH^2))])^2))/(MH^2))};

listA={j[RA,0,1,1],j[RA,0,1,1],j[RA,1,0,0],j[RA,0,1,0],j[RA,0,0,1],j[RA,-1,1,1],j[RA,1,1,1],j[RA,1,1,1]};
coefA={((48 m)/(-2+D)),-((8 D m)/(-2+D)),((32 m)/((-2+D) (MH^2))),-((32 m)/((-2+D) (MH^2))),-((32 m)/((-2+D) (MH^2))),((32 m)/((-2+D) (MH^2))),((8 m (MH^2))/(-2+D)),-((4 D m (MH^2))/(-2+D))};

tmp=listA*coefA;
amp=0;
Do[amp=amp+tmp[[i]],{i,1,Length[tmp]}]

(amp/m)/.reps//Simplify//Series[#,{ϵ,0,0}]&

Comparison with analytic result from Feynman parameter evaluation:

Series[-4(-((μ^2)/(MH^2)))^(ϵ)Exp[ϵ EulerGamma](1-3ϵ)2Gamma[1+ϵ]((Gamma[-ϵ]^2)/(Gamma[3-2ϵ])),{ϵ,0,0}]

Quit

2-Loop Result

Numerator expressions in terms of propagators

num21=2*I*SUNT[a,c,d,b].SUNDelta[c,d]*TR[(GSD[k]+m).GAD[μ].(GSD[k+p1]+m).GAD[α].(GSD[l+p1]+m).(GSD[l-p2]+m).GAD[β].(GSD[k-p2]+m).GAD[ν]].MTD[α,β].((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

tmp2=2*I*SUNT[c,a,d,b].SUNDelta[c,d]*TR[(GSD[k]+m).GAD[α].(GSD[l]+m).GAD[μ].(GSD[l+p1]+m).GAD[β].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[ν]].MTD[α,β]//Contract//SUNSimplify;
num22=tmp2.MTDperp[μ,ν]//Contract//SUNSimplify//Simplify;

num23=2*I*SUNT[c,d,a,b].SUNDelta[c,d]*TR[(GSD[k]+m).GAD[μ].(GSD[k+p1]+m).GAD[α].(GSD[l+p1]+m).GAD[β].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[ν]].MTD[α,β].((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

num24=2*I*SUNT[c,d,a,b].SUNDelta[c,d]*TR[(GSD[k]+m).GAD[α].(GSD[l]+m).GAD[β].(GSD[k]+m).GAD[μ].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[ν]].MTD[α,β].((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

num25=2*(-I)*SUNT[c,d].SUNDelta[c,e].SUNDelta[d,f].SUNDelta[g,h].SUNF[a,g,e].SUNF[b,f,h]*TR[(-GSD[l-k]+m).GAD[ρ].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[λ]].MTD[ρ,γ].MTD[λ,δ].MTD[α,β].(2MTD[μ,γ].FVD[p1,α]+MTD[α,γ].FVD[-2l-p1,μ]-2MTD[μ,α].FVD[p1,γ]).(2MTD[ν,β].FVD[p2,δ]+MTD[β,δ].FVD[-2l+p2,ν]-2MTD[ν,δ].FVD[p2,β]).((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

num26=2*(-1)*SUNT[c,d,b].SUNDelta[c,e].SUNDelta[d,f].SUNF[a,e,f]*TR[(GSD[k]+m).GAD[α].(-GSD[l-k]+m).GAD[β].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[ν]].MTD[β,γ].MTD[α,δ].(2MTD[μ,γ].FVD[p1,δ]+MTD[γ,δ].FVD[-2l-p1,μ]-2MTD[μ,δ].FVD[p1,γ]).((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

num27=2*(-1)*(1/2)I CA CF*TR[(GSD[k]+m).GAD[μ].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[α].(GSD[k-l]+m).GAD[β]].MTD[α,γ].MTD[β,δ].(MTD[γ,ν].FVD[-l+2p2,δ]+MTD[ν,δ].FVD[-p2-l,γ]+MTD[δ,γ].FVD[2l-p2,ν]).(MTD[μ,ν]-(1/(Pair[Momentum[n,D],Momentum[nb,D]]))(FVD[n,μ]FVD[nb,ν]+FVD[nb,μ]FVD[n,ν]))//Contract//SUNSimplify;

num28=(-I)*SUNT[c,d].SUNDelta[c,e].SUNDelta[d,f].TR[(-GSD[l-k]+m).GAD[α].(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[β]].MTD[α,γ].MTD[β,δ].(SUNF[a,f,x].SUNF[x,b,e](MTD[μ,ν].MTD[γ,δ]-MTD[μ,δ].MTD[ν,γ]+MTD[μ,γ].MTD[ν,δ])+SUNF[a,e,x].SUNF[x,f,b](MTD[μ,γ].MTD[ν,δ]-MTD[μ,ν].MTD[γ,δ]-MTD[μ,δ].MTD[ν,γ])+SUNF[a,b,x].SUNF[x,f,e](MTD[μ,γ].MTD[ν,δ]-MTD[μ,δ].MTD[ν,γ])).((MTDperp[μ,ν])/(D-2))//Contract//SUNSimplify;

num29=(I/2)CF CA*TR[(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[α].(GSD[k-l-p2]+m).GAD[ν].(GSD[k-l]+m).GAD[γ]].MTD[α,β].MTD[γ,δ].(MTD[δ,μ].FVD[l+2p1,β]-MTD[μ,β].FVD[l-p1,δ]+MTD[β,δ].FVD[-2l-p1,μ]).(MTD[μ,ν]-(1/(Pair[Momentum[n,D],Momentum[nb,D]]))(FVD[n,μ]FVD[nb,ν]+FVD[nb,μ]FVD[n,ν]))//Contract//SUNSimplify;

num210=(I/2)CF CA*TR[(GSD[k+p1]+m).(GSD[k-p2]+m).GAD[α].(GSD[l]+m).GAD[μ].(GSD[l+p1]+m).GAD[γ]].MTD[γ,δ].MTD[α,β].(MTD[ν,δ].FVD[-p2-k+l,β]+MTD[δ,β].FVD[2k-2l-p2,ν]+MTD[β,ν].FVD[-k+l+2p2,δ]).(MTD[μ,ν]-(1/(Pair[Momentum[n,D],Momentum[nb,D]]))(FVD[n,μ]FVD[nb,ν]+FVD[nb,μ]FVD[n,ν]))//Contract;

numplan=(num21/(D1 D3 D4 D5 D6 D7))+(num22/(D1 D2 D3 D4 D5 D7))+(num23/(D1 D3^2 D4 D5 D7))+(num24/(D1^2 D2 D3 D4 D7))+(num25/(D2 D3 D4 D5 D6 D7))+(num26/(D1 D2 D3 D4 D5 D7))+(num27/(D1 D2 D3 D4 D5 D7))+(num28/(D3 D4 D5 D6 D7));

numplan=Coefficient[numplan,m]*m;

numnonplan=(num29/(D1 D2 D3 D4 D6 D7))+(num210/(D1 D2 D3 D4 D6 D7));

numnonplan=Coefficient[numnonplan,m]*m;

We have already projected out the correct Dirac and Lorentz structure with MTDperp. Now we need to express the numerators in terms of propagators. We define the following nomenclature: planar topology: ( (k^2)=(Subscript[D, 1]), (l^2)=(Subscript[D, 2]), (((k+(Subscript[p, 1])))^2)=(Subscript[D, 3]), (((k-(Subscript[p, 2])))^2)=(Subscript[D, 4]), (((l+(Subscript[p, 1])))^2)=(Subscript[D, 5]), (((l-(Subscript[p, 2])))^2)=(Subscript[D, 6]), (((k-l))^2)=(Subscript[D, 7])) and nonplanar topology: ((l^2)=(Subscript[D, 1]), (((k+(Subscript[p, 1])))^2)=(Subscript[D, 2]), (((k-(Subscript[p, 2])))^2)=(Subscript[D, 3]), (((l+(Subscript[p, 1])))^2)=(Subscript[D, 4]), (((l+(Subscript[p, 2])))^2)=(Subscript[D, 5]), (((k-l))^2)=(Subscript[D, 6]), (((k-l-(Subscript[p, 2])))^2)=(Subscript[D, 7])).

momrepsplan={Pair[Momentum[n,D],Momentum[n,D]]->0,Pair[Momentum[n,D],Momentum[nb,D]]->2,Pair[Momentum[nb,D],Momentum[nb,D]]->0,Pair[Momentum[p1,D],Momentum[p1,D]]->0,Pair[Momentum[p2,D],Momentum[p2,D]]->0,Pair[Momentum[p1,D],Momentum[p2,D]]->((MH^2)/2),Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[nb,D],Momentum[p1,D]]->MH,Pair[Momentum[n,D],Momentum[p2,D]]->MH,Pair[Momentum[nb,D],Momentum[p2,D]]->0,Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[k,D],Momentum[k,D]]->D1,Pair[Momentum[l,D],Momentum[l,D]]->D2,Pair[Momentum[k,D],Momentum[p1,D]]->(1/2)(D3-D1),Pair[Momentum[k,D],Momentum[p2,D]]->((-1)/2)(D4-D1),Pair[Momentum[l,D],Momentum[p1,D]]->(1/2)(D5-D2),Pair[Momentum[l,D],Momentum[p2,D]]->((-1)/2)(D6-D2),Pair[Momentum[k,D],Momentum[l,D]]->(1/2)(D1+D2-D7),Pair[Momentum[nb,D],Momentum[k,D]]->((-1)/MH)(D4-D1),Pair[Momentum[n,D],Momentum[k,D]]->(1/MH)(D3-D1),Pair[Momentum[nb,D],Momentum[l,D]]->((-1)/MH)(D6-D2),Pair[Momentum[n,D],Momentum[l,D]]->(1/MH)(D5-D2)};

numplan=numplan/.momrepsplan;

momrepsnonplan={Pair[Momentum[n,D],Momentum[n,D]]->0,Pair[Momentum[n,D],Momentum[nb,D]]->2,Pair[Momentum[nb,D],Momentum[nb,D]]->0,Pair[Momentum[p1,D],Momentum[p1,D]]->0,Pair[Momentum[p2,D],Momentum[p2,D]]->0,Pair[Momentum[p1,D],Momentum[p2,D]]->((MH^2)/2),Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[nb,D],Momentum[p1,D]]->MH,Pair[Momentum[n,D],Momentum[p2,D]]->MH,Pair[Momentum[nb,D],Momentum[p2,D]]->0,Pair[Momentum[n,D],Momentum[p1,D]]->0,Pair[Momentum[l,D],Momentum[l,D]]->D1,Pair[Momentum[l,D],Momentum[p1,D]]->(1/2)(D4-D1),Pair[Momentum[l,D],Momentum[p2,D]]->(1/2)(D5-D1),Pair[Momentum[l,D],Momentum[k,D]]->(1/2)(D3+D5-D7),Pair[Momentum[k,D],Momentum[k,D]]->D3-D7+D5-D1+D6,Pair[Momentum[k,D],Momentum[p1,D]]->(1/2)(D2-D3+D7-D5+D1-D6),Pair[Momentum[k,D],Momentum[p2,D]]->((-1)/2)(D7-D5+D1-D6),Pair[Momentum[l,D],Momentum[n,D]]->(1/MH)(D4-D1),Pair[Momentum[l,D],Momentum[nb,D]]->(1/MH)(D5-D1),Pair[Momentum[k,D],Momentum[n,D]]->(1/MH)(D2-D3+D7-D5+D1-D6),Pair[Momentum[k,D],Momentum[nb,D]]->((-1)/MH)(D7-D5+D1-D6)};

numnonplan=numnonplan/.momrepsnonplan;

Reduction to scalar integrals

planar topology

numplan//Variables

The following code snippet now turns the planar topology into a sum consistent of scalar integrals that all follow the form j[topology,a,b,c,d,e,f,g]=∫dk∫dl(1/(((Subscript[D, 1])^a)((Subscript[D, 2])^b)((Subscript[D, 3])^c)((Subscript[D, 4])^d)((Subscript[D, 5])^e)((Subscript[D, 6])^f)((Subscript[D, 7])^g))).

tmp=numplan//Expand;
Do[exp1[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D1]],{i1,1,Length[tmp]}]
Do[exp2[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D2]],{i1,1,Length[tmp]}]
Do[exp3[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D3]],{i1,1,Length[tmp]}]
Do[exp4[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D4]],{i1,1,Length[tmp]}]
Do[exp5[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D5]],{i1,1,Length[tmp]}]
Do[exp6[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D6]],{i1,1,Length[tmp]}]
Do[exp7[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D7]],{i1,1,Length[tmp]}]
listplan=List[];
Do[listplan=Append[listplan,j[plan,-exp1[i1],-exp2[i1],-exp3[i1],-exp4[i1],-exp5[i1],-exp6[i1],-exp7[i1]]],{i1,1,Length[tmp]}]
coefplan=List[];
Do[coefplan=Append[coefplan,tmp[[i1]]*(D1^(-exp1[i1]))*(D2^(-exp2[i1]))*(D3^(-exp3[i1]))*(D4^(-exp4[i1]))*(D5^(-exp5[i1]))*(D6^(-exp6[i1]))*(D7^(-exp7[i1]))],{i1,1,Length[tmp]}]

listplan//Variables//StandardForm

listplan//StandardForm

coefplan//StandardForm

nonplanar topology

numnonplan//Variables

tmp=numnonplan//Expand;
Do[exp1[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D1]],{i1,1,Length[tmp]}]
Do[exp2[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D2]],{i1,1,Length[tmp]}]
Do[exp3[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D3]],{i1,1,Length[tmp]}]
Do[exp4[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D4]],{i1,1,Length[tmp]}]
Do[exp5[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D5]],{i1,1,Length[tmp]}]
Do[exp6[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D6]],{i1,1,Length[tmp]}]
Do[exp7[i1]=Coefficient[PowerExpand[Log[tmp[[i1]]]],Log[D7]],{i1,1,Length[tmp]}]
listnonplan=List[];
Do[listnonplan=Append[listnonplan,j[nonplan,-exp1[i1],-exp2[i1],-exp3[i1],-exp4[i1],-exp5[i1],-exp6[i1],-exp7[i1]]],{i1,1,Length[tmp]}]
coefnonplan=List[];
Do[coefnonplan=Append[coefnonplan,tmp[[i1]]*(D1^(-exp1[i1]))*(D2^(-exp2[i1]))*(D3^(-exp3[i1]))*(D4^(-exp4[i1]))*(D5^(-exp5[i1]))*(D6^(-exp6[i1]))*(D7^(-exp7[i1]))],{i1,1,Length[tmp]}]

listnonplan//Variables//StandardForm

listnonplan//StandardForm

coefnonplan//StandardForm

Reduction to Master Integrals with IBP relations

Quit[]

<<LiteRed2024`;
SetDirectory[NotebookDirectory[]];
SetDim[d];
Declare[{l,k,p1,p2},Vector,{mH},Number];
SetConstraints[{p1,p2},sp[p1]=0;sp[p2]=0;sp[p1,p2]=((mH^2)/2);
];

NewDsBasis[plan,{k,l,sp[k+p1],sp[k-p2],sp[l+p1],sp[l-p2],sp[l-k]},{l,k},GenerateIBP->True,AnalyzeSectors->True,FindSymmetries->True,SolvejSector->True,Directory->"plan dir"]
DiskSave[plan]

Cut propagators can be implemented with e.g. CutDs->{1,0,0,0,0,0,0}

NewDsBasis[nonplan,{l,sp[k+p1],sp[k-p2],sp[l+p1],sp[l+p2],sp[l-k],sp[k-l-p2]},{l,k},GenerateIBP->True,AnalyzeSectors->True,FindSymmetries->True,SolvejSector->True,Directory->"nonplan dir"]
DiskSave[nonplan]

If you already generated the IBP rules and saved them in the respective directory, just load them to the notebook here:

(*Quit[]*)

(*<<LiteRed2024`;
SetDirectory[NotebookDirectory[]];
SetDim[d];
Declare[{l,k,p1,p2},Vector,{mH},Number];
SetConstraints[{p1,p2},
sp[p1]=0;sp[p2]=0;sp[p1,p2]=((mH^2)/2);
];
<<"plan dir/plan";
<<"nonplan dir/nonplan"*)

Load lists and coefficients from above

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,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,1,0,0,1,1,-1,1],j[plan,0,1,0,1,1,-1,1],j[plan,0,1,0,1,1,-1,1],j[plan,0,1,0,1,1,-1,1],j[plan,0,1,0,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,0,0,1,1,1,-1,1],j[plan,-1,1,1,1,1,-1,1],j[plan,-1,1,1,1,1,-1,1],j[plan,-1,1,1,1,1,-1,1],j[plan,-1,1,1,1,1,-1,1],j[plan,1,1,-1,1,1,-1,1],j[plan,1,1,-1,1,1,-1,1],j[plan,1,1,-1,1,1,-1,1],j[plan,1,1,0,1,1,-2,1],j[plan,1,1,0,1,1,-2,1],j[plan,0,1,1,1,1,-2,1],j[plan,0,1,1,1,1,-2,1],j[plan,2,1,1,1,0,0,0],j[plan,2,1,1,1,0,0,0],j[plan,2,1,1,1,0,0,0],j[plan,1,0,2,1,1,0,0],j[plan,1,0,2,1,1,0,0],j[plan,1,0,2,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,1,1,1,1,0,0],j[plan,1,0,1,1,1,1,0],j[plan,1,0,1,1,1,1,0],j[plan,0,1,1,1,1,1,0],j[plan,0,1,1,1,1,1,0],j[plan,1,0,2,1,0,0,1],j[plan,1,0,2,1,0,0,1],j[plan,1,0,2,1,0,0,1],j[plan,2,0,1,1,0,0,1],j[plan,2,0,1,1,0,0,1],j[plan,2,0,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,1,0,0,1],j[plan,1,1,1,0,1,0,1],j[plan,1,1,1,0,1,0,1],j[plan,1,1,0,1,1,0,1],j[plan,1,1,0,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,1,0,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,0,1,1,1,1,0,1],j[plan,1,0,1,1,0,1,1],j[plan,1,0,1,1,0,1,1],j[plan,0,1,1,1,0,1,1],j[plan,0,1,1,1,0,1,1],j[plan,0,0,1,1,1,1,1],j[plan,0,0,1,1,1,1,1],j[plan,0,0,1,1,1,1,1],j[plan,0,0,1,1,1,1,1],j[plan,0,0,1,1,1,1,1],j[plan,1,-1,1,1,1,1,1],j[plan,1,-1,1,1,1,1,1],j[plan,1,1,1,1,1,-1,1],j[plan,1,1,1,1,1,-1,1],j[plan,1,0,1,1,1,1,1],j[plan,1,0,1,1,1,1,1],j[plan,0,1,1,1,1,1,1],j[plan,0,1,1,1,1,1,1]};

coefplan={8 I CA CF m,-16 I (CF^2) m,((8 I CA CF m)/(-2+D)),-((32 I (CF^2) m)/(-2+D)),-4 I CA CF D m,8 I (CF^2) D m,-((4 I CA CF D m)/(-2+D)),((16 I (CF^2) D m)/(-2+D)),12 I CA CF m,8 I CA CF m,-16 I (CF^2) m,-((8 I CA CF m)/(-2+D)),-((96 I (CF^2) m)/(-2+D)),((64 I (CF^2) D m)/(-2+D)),-((8 I (CF^2) (D^2) m)/(-2+D)),-48 I (CF^2) m,((24 I CA CF m)/(-2+D)),((16 I (CF^2) m)/(-2+D)),24 I (CF^2) D m,-((12 I CA CF D m)/(-2+D)),-((8 I (CF^2) D m)/(-2+D)),-24 I CA CF m,-48 I (CF^2) m,((16 I CA CF m)/(-2+D)),24 I (CF^2) D m,-((8 I CA CF D m)/(-2+D)),((16 I (CF^2) m)/(-2+D)),-((8 I (CF^2) D m)/(-2+D)),((16 I (CF^2) m)/(-2+D)),-((8 I (CF^2) D m)/(-2+D)),-16 I CA CF m,((64 I CA CF m)/(-2+D)),-((96 I (CF^2) m)/(-2+D)),8 I CA CF D m,-((32 I CA CF D m)/(-2+D)),((64 I (CF^2) D m)/(-2+D)),-((8 I (CF^2) (D^2) m)/(-2+D)),-8 I CA CF m,4 I CA CF D m,-28 I CA CF m,24 I (CF^2) m,((4 I CA CF m)/(-2+D)),10 I CA CF D m,-8 I (CF^2) D m,-((8 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),-((8 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),((96 I (CF^2) m)/(-2+D)),-((64 I (CF^2) D m)/(-2+D)),((8 I (CF^2) (D^2) m)/(-2+D)),-8 I CA CF m,32 I (CF^2) m,-((16 I CA CF m)/(-2+D)),((64 I (CF^2) m)/(-2+D)),4 I CA CF D m,-16 I (CF^2) D m,((8 I CA CF D m)/(-2+D)),-((48 I (CF^2) D m)/(-2+D)),((8 I (CF^2) (D^2) m)/(-2+D)),44 I CA CF m,-56 I (CF^2) m,-((12 I CA CF m)/(-2+D)),((32 I (CF^2) m)/(-2+D)),-22 I CA CF D m,32 I (CF^2) D m,-((12 I CA CF D m)/(-2+D)),-((16 I (CF^2) D m)/(-2+D)),2 I CA CF (D^2) m,-4 I (CF^2) (D^2) m,32 I CA CF m,-64 I (CF^2) m,-16 I CA CF D m,32 I (CF^2) D m,2 I CA CF (D^2) m,-4 I (CF^2) (D^2) m,16 I CA CF m,-24 I (CF^2) m,-((4 I CA CF m)/(-2+D)),-10 I CA CF D m,8 I (CF^2) D m,((8 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),-36 I CA CF m,64 I (CF^2) m,20 I CA CF D m,-32 I (CF^2) D m,-2 I CA CF (D^2) m,4 I (CF^2) (D^2) m,32 I CA CF m,-56 I (CF^2) m,-((12 I CA CF m)/(-2+D)),-20 I CA CF D m,40 I (CF^2) D m,((8 I CA CF D m)/(-2+D)),-((16 I (CF^2) D m)/(-2+D)),2 I CA CF (D^2) m,-4 I (CF^2) (D^2) m,((4 I (CF^2) (D^2) m)/(-2+D)),-24 I CA CF m,48 I (CF^2) m,((120 I CA CF m)/(-2+D)),4 I CA CF D m,-8 I (CF^2) D m,-((24 I CA CF D m)/(-2+D)),-56 I CA CF m,48 I (CF^2) m,((144 I (CF^2) m)/(-2+D)),16 I CA CF D m,-16 I (CF^2) D m,((20 I CA CF D m)/(-2+D)),-((40 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),32 I CA CF m,-16 I (CF^2) m,-((112 I CA CF m)/(-2+D)),-8 I CA CF D m,((24 I CA CF D m)/(-2+D)),-((32 I (CF^2) m)/(-2+D)),((24 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),-((16 I (CF^2) m)/(-2+D)),((16 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),-((16 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),((96 I CA CF m)/(-2+D)),-((16 I CA CF D m)/(-2+D)),8 I CA CF m,-((32 I CA CF m)/(-2+D)),((64 I (CF^2) m)/(-2+D)),-4 I CA CF D m,((32 I CA CF D m)/(-2+D)),-((8 I (CF^2) D m)/(-2+D)),-((96 I CA CF m)/(-2+D)),((16 I CA CF D m)/(-2+D)),-((32 I (CF^2) m)/(-2+D)),-((128 I CA CF m)/(-2+D)),((32 I CA CF D m)/(-2+D)),-8 I CA CF m,-((64 I CA CF m)/(-2+D)),((64 I (CF^2) m)/(-2+D)),((16 I CA CF D m)/(-2+D)),-((24 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),((128 I CA CF m)/(-2+D)),-((32 I CA CF D m)/(-2+D)),-((16 I (CF^2) m)/(-2+D)),((24 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),-8 I CA CF m,-((64 I CA CF m)/(-2+D)),((64 I (CF^2) m)/(-2+D)),((16 I CA CF D m)/(-2+D)),-((24 I (CF^2) D m)/(-2+D)),((4 I (CF^2) (D^2) m)/(-2+D)),((128 I CA CF m)/(-2+D)),-((32 I CA CF D m)/(-2+D)),-((16 I (CF^2) m)/(-2+D)),((24 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),((192 I CA CF m)/(-2+D)),-((32 I (CF^2) m)/(-2+D)),-((32 I CA CF D m)/(-2+D)),-((128 I CA CF m)/(-2+D)),((32 I CA CF D m)/(-2+D)),-((32 I (CF^2) m)/(-2+D)),-((16 I CA CF D m)/(-2+D)),-16 I (CF^2) m,((8 I CA CF m)/(-2+D)),-((16 I (CF^2) m)/(-2+D)),8 I (CF^2) D m,-((4 I CA CF D m)/(-2+D)),((16 I (CF^2) D m)/(-2+D)),-((4 I (CF^2) (D^2) m)/(-2+D)),-40 I CA CF m,72 I (CF^2) m,((20 I CA CF m)/(-2+D)),20 I CA CF D m,-40 I (CF^2) D m,-((8 I CA CF D m)/(-2+D)),-2 I 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(MH^2))/(-2+D)),-((16 I (CF^2) m (MH^2))/(-2+D)),((16 I (CF^2) D m (MH^2))/(-2+D)),-((4 I (CF^2) (D^2) m (MH^2))/(-2+D)),48 I CA CF m (MH^2),-72 I (CF^2) m (MH^2),-((20 I CA CF m (MH^2))/(-2+D)),-24 I CA CF D m (MH^2),40 I (CF^2) D m (MH^2),((8 I CA CF D m (MH^2))/(-2+D)),2 I CA CF (D^2) m (MH^2),-4 I (CF^2) (D^2) m (MH^2),((16 I (CF^2) D m (MH^2))/(-2+D)),-((4 I (CF^2) (D^2) m (MH^2))/(-2+D)),-((128 I CA CF m (MH^2))/(-2+D)),((32 I CA CF D m (MH^2))/(-2+D)),((16 I (CF^2) m (MH^2))/(-2+D)),-((16 I (CF^2) D m (MH^2))/(-2+D)),((4 I (CF^2) (D^2) m (MH^2))/(-2+D)),((16 I (CF^2) m (MH^2))/(-2+D)),-((16 I (CF^2) D m (MH^2))/(-2+D)),((4 I (CF^2) (D^2) m (MH^2))/(-2+D)),-8 I CA CF m (MH^2),16 I (CF^2) m (MH^2),((8 I CA CF m (MH^2))/(-2+D)),((16 I (CF^2) m (MH^2))/(-2+D)),4 I CA CF D m (MH^2),-8 I (CF^2) D m (MH^2),-((4 I CA CF D m (MH^2))/(-2+D)),-((8 I (CF^2) D m (MH^2))/(-2+D)),8 I CA CF m (MH^2),-4 I CA CF D m (MH^2),-((8 I CA CF m (MH^2))/(-2+D)),((4 I CA CF D m (MH^2))/(-2+D)),-32 I CA CF m (MH^2),24 I (CF^2) m (MH^2),((20 I CA CF m (MH^2))/(-2+D)),((16 I (CF^2) m (MH^2))/(-2+D)),12 I CA CF D m (MH^2),-8 I (CF^2) D m (MH^2),-((8 I CA CF D m (MH^2))/(-2+D)),-((8 I (CF^2) D m (MH^2))/(-2+D)),-12 I CA CF m (MH^2),8 I (CF^2) m (MH^2),((28 I CA CF m (MH^2))/(-2+D)),6 I CA CF D m (MH^2),-8 I (CF^2) D m (MH^2),-((12 I CA CF D m (MH^2))/(-2+D)),((16 I (CF^2) m (MH^2))/(-2+D)),-((8 I (CF^2) D m (MH^2))/(-2+D)),((16 I CA CF m (MH^2))/(-2+D)),-((8 I CA CF D m (MH^2))/(-2+D)),((96 I CA CF m (MH^2))/(-2+D)),-((64 I (CF^2) m (MH^2))/(-2+D)),4 I CA CF D m (MH^2),-((32 I CA CF D m (MH^2))/(-2+D)),((8 I (CF^2) D m (MH^2))/(-2+D)),-((32 I (CF^2) m (MH^2))/(-2+D)),((8 I (CF^2) D m (MH^2))/(-2+D)),-8 I CA CF m (MH^2),4 I CA CF D m (MH^2),-((16 I (CF^2) m (MH^4))/(-2+D)),((8 I (CF^2) D m (MH^4))/(-2+D)),-((16 I CA CF m (MH^4))/(-2+D)),((8 I CA CF D m (MH^4))/(-2+D))}

listnonplan={j[nonplan,1,1,1,1,0,0,0],j[nonplan,1,1,1,1,0,0,0],j[nonplan,1,1,1,0,0,1,0],j[nonplan,1,1,1,0,0,1,0],j[nonplan,1,1,0,1,0,1,0],j[nonplan,1,1,0,1,0,1,0],j[nonplan,1,0,1,1,0,1,0],j[nonplan,1,0,1,1,0,1,0],j[nonplan,0,1,1,1,0,1,0],j[nonplan,0,1,1,1,0,1,0],j[nonplan,1,1,1,1,-1,1,0],j[nonplan,1,1,1,1,-1,1,0],j[nonplan,1,1,1,0,0,0,1],j[nonplan,1,1,1,0,0,0,1],j[nonplan,1,1,0,1,0,0,1],j[nonplan,1,1,0,1,0,0,1],j[nonplan,1,0,1,1,0,0,1],j[nonplan,1,0,1,1,0,0,1],j[nonplan,0,1,1,1,0,0,1],j[nonplan,0,1,1,1,0,0,1],j[nonplan,1,1,1,1,-1,0,1],j[nonplan,1,1,1,1,-1,0,1],j[nonplan,1,1,0,0,0,1,1],j[nonplan,1,0,1,0,0,1,1],j[nonplan,1,0,1,0,0,1,1],j[nonplan,0,1,1,0,0,1,1],j[nonplan,0,1,1,0,0,1,1],j[nonplan,1,0,0,1,0,1,1],j[nonplan,0,1,0,1,0,1,1],j[nonplan,0,1,0,1,0,1,1],j[nonplan,0,0,1,1,0,1,1],j[nonplan,0,0,1,1,0,1,1],j[nonplan,-1,1,1,1,0,1,1],j[nonplan,1,-1,1,1,0,1,1],j[nonplan,1,-1,1,1,0,1,1],j[nonplan,1,1,-1,1,0,1,1],j[nonplan,1,1,-1,1,0,1,1],j[nonplan,1,1,1,-1,0,1,1],j[nonplan,1,1,1,-1,0,1,1],j[nonplan,1,1,1,0,-1,1,1],j[nonplan,1,1,1,0,-1,1,1],j[nonplan,1,1,0,1,-1,1,1],j[nonplan,1,0,1,1,-1,1,1],j[nonplan,1,0,1,1,-1,1,1],j[nonplan,0,1,1,1,-1,1,1],j[nonplan,0,1,1,1,-1,1,1],j[nonplan,1,1,1,1,-2,1,1],j[nonplan,1,1,1,1,-2,1,1],j[nonplan,1,1,1,1,0,-1,1],j[nonplan,1,1,1,1,0,-1,1],j[nonplan,1,1,1,1,0,1,-1],j[nonplan,1,1,1,1,0,1,-1],j[nonplan,1,1,1,0,0,0,0],j[nonplan,1,1,1,0,0,0,0],j[nonplan,1,1,0,1,0,0,0],j[nonplan,1,0,1,1,0,0,0],j[nonplan,0,1,1,1,0,0,0],j[nonplan,0,1,1,1,0,0,0],j[nonplan,1,1,1,1,-1,0,0],j[nonplan,1,1,0,0,0,1,0],j[nonplan,1,1,0,0,0,1,0],j[nonplan,1,0,1,0,0,1,0],j[nonplan,1,0,1,0,0,1,0],j[nonplan,0,1,1,0,0,1,0],j[nonplan,0,1,1,0,0,1,0],j[nonplan,1,0,0,1,0,1,0],j[nonplan,0,1,0,1,0,1,0],j[nonplan,0,1,0,1,0,1,0],j[nonplan,0,0,1,1,0,1,0],j[nonplan,0,0,1,1,0,1,0],j[nonplan,-1,1,1,1,0,1,0],j[nonplan,-1,1,1,1,0,1,0],j[nonplan,1,-1,1,1,0,1,0],j[nonplan,1,1,-1,1,0,1,0],j[nonplan,1,1,1,-1,0,1,0],j[nonplan,1,1,1,-1,0,1,0],j[nonplan,1,1,1,0,-1,1,0],j[nonplan,1,1,1,0,-1,1,0],j[nonplan,1,1,0,1,-1,1,0],j[nonplan,1,1,0,1,-1,1,0],j[nonplan,1,0,1,1,-1,1,0],j[nonplan,1,0,1,1,-1,1,0],j[nonplan,0,1,1,1,-1,1,0],j[nonplan,0,1,1,1,-1,1,0],j[nonplan,1,1,1,1,-2,1,0],j[nonplan,1,1,1,1,-2,1,0],j[nonplan,1,1,1,1,0,-1,0],j[nonplan,1,1,0,0,0,0,1],j[nonplan,1,1,0,0,0,0,1],j[nonplan,1,0,1,0,0,0,1],j[nonplan,1,0,1,0,0,0,1],j[nonplan,0,1,1,0,0,0,1],j[nonplan,0,1,1,0,0,0,1],j[nonplan,1,0,0,1,0,0,1],j[nonplan,0,1,0,1,0,0,1],j[nonplan,0,1,0,1,0,0,1],j[nonplan,0,0,1,1,0,0,1],j[nonplan,0,0,1,1,0,0,1],j[nonplan,-1,1,1,1,0,0,1],j[nonplan,1,-1,1,1,0,0,1],j[nonplan,1,1,-1,1,0,0,1],j[nonplan,1,1,1,-1,0,0,1],j[nonplan,1,1,1,-1,0,0,1],j[nonplan,1,1,1,0,-1,0,1],j[nonplan,1,1,1,0,-1,0,1],j[nonplan,1,1,0,1,-1,0,1],j[nonplan,1,1,0,1,-1,0,1],j[nonplan,1,0,1,1,-1,0,1],j[nonplan,1,0,1,1,-1,0,1],j[nonplan,0,1,1,1,-1,0,1],j[nonplan,0,1,1,1,-1,0,1],j[nonplan,1,1,1,1,-2,0,1],j[nonplan,1,1,1,1,-2,0,1],j[nonplan,0,1,0,0,0,1,1],j[nonplan,0,0,1,0,0,1,1],j[nonplan,0,0,1,0,0,1,1],j[nonplan,-1,1,1,0,0,1,1],j[nonplan,-1,1,1,0,0,1,1],j[nonplan,0,0,0,1,0,1,1],j[nonplan,-1,1,0,1,0,1,1],j[nonplan,-1,1,0,1,0,1,1],j[nonplan,-1,0,1,1,0,1,1],j[nonplan,-1,0,1,1,0,1,1],j[nonplan,-2,1,1,1,0,1,1],j[nonplan,-2,1,1,1,0,1,1],j[nonplan,0,-1,1,1,0,1,1],j[nonplan,0,1,-1,1,0,1,1],j[nonplan,0,1,1,-1,0,1,1],j[nonplan,0,1,1,-1,0,1,1],j[nonplan,1,1,0,0,-1,1,1],j[nonplan,1,0,1,0,-1,1,1],j[nonplan,1,0,1,0,-1,1,1],j[nonplan,0,1,1,0,-1,1,1],j[nonplan,0,1,1,0,-1,1,1],j[nonplan,1,0,0,1,-1,1,1],j[nonplan,0,1,0,1,-1,1,1],j[nonplan,0,1,0,1,-1,1,1],j[nonplan,0,0,1,1,-1,1,1],j[nonplan,0,0,1,1,-1,1,1],j[nonplan,-1,1,1,1,-1,1,1],j[nonplan,-1,1,1,1,-1,1,1],j[nonplan,1,-1,1,1,-1,1,1],j[nonplan,1,1,-1,1,-1,1,1],j[nonplan,1,1,1,-1,-1,1,1],j[nonplan,1,1,1,-1,-1,1,1],j[nonplan,1,1,1,0,-2,1,1],j[nonplan,1,1,1,0,-2,1,1],j[nonplan,1,1,0,1,-2,1,1],j[nonplan,1,0,1,1,-2,1,1],j[nonplan,0,1,1,1,-2,1,1],j[nonplan,0,1,1,1,-2,1,1],j[nonplan,1,1,1,1,-3,1,1],j[nonplan,1,1,1,0,0,-1,1],j[nonplan,1,1,1,0,0,-1,1],j[nonplan,1,1,0,1,0,-1,1],j[nonplan,1,0,1,1,0,-1,1],j[nonplan,0,1,1,1,0,-1,1],j[nonplan,0,1,1,1,0,-1,1],j[nonplan,1,1,1,1,-1,-1,1],j[nonplan,1,1,1,1,-1,-1,1],j[nonplan,1,1,1,1,0,-2,1],j[nonplan,1,1,1,1,0,0,-1],j[nonplan,1,1,1,0,0,1,-1],j[nonplan,1,1,1,0,0,1,-1],j[nonplan,1,1,0,1,0,1,-1],j[nonplan,1,0,1,1,0,1,-1],j[nonplan,0,1,1,1,0,1,-1],j[nonplan,0,1,1,1,0,1,-1],j[nonplan,1,1,1,1,-1,1,-1],j[nonplan,1,1,1,1,-1,1,-1],j[nonplan,1,1,1,1,0,1,-2],j[nonplan,1,1,1,1,0,1,0],j[nonplan,1,1,1,1,0,1,0],j[nonplan,1,1,1,1,0,0,1],j[nonplan,1,1,1,1,0,0,1],j[nonplan,1,1,1,0,0,1,1],j[nonplan,1,1,1,0,0,1,1],j[nonplan,1,1,0,1,0,1,1],j[nonplan,1,1,0,1,0,1,1],j[nonplan,1,0,1,1,0,1,1],j[nonplan,1,0,1,1,0,1,1],j[nonplan,0,1,1,1,0,1,1],j[nonplan,0,1,1,1,0,1,1],j[nonplan,1,1,1,1,-1,1,1]};

coefnonplan={80 I CA CF m,-6 I CA CF D m,26 I CA CF m,I CA CF D m,22 I CA CF m,5 I CA CF D m,-22 I CA CF m,-I CA CF D m,-44 I CA CF m,-12 I CA CF D m,10 I CA CF m,9 I CA CF D m,-54 I CA CF m,7 I CA CF D m,-58 I CA CF m,5 I CA CF D m,54 I CA CF m,-5 I CA CF D m,108 I CA CF m,-6 I CA CF D m,-62 I CA CF m,5 I CA CF D m,-2 I CA CF D m,-4 I CA CF m,2 I CA CF D m,30 I CA CF m,I CA CF D m,2 I CA CF D m,12 I CA CF m,6 I CA CF D m,-4 I CA CF m,-4 I CA CF D m,-44 I CA CF m,2 I CA CF m,-I CA CF D m,-6 I CA CF m,-I CA CF D m,2 I CA CF m,-I CA CF D m,-18 I CA CF m,-I CA CF D m,-6 I CA CF D m,-8 I CA CF m,4 I CA CF D m,34 I CA CF m,5 I CA CF D m,4 I CA CF m,-4 I CA CF D m,-56 I CA CF m,6 I CA CF D m,-16 I CA CF m,-4 I CA CF D m,((88 I CA CF m)/(MH^2)),-((8 I CA CF D m)/(MH^2)),((96 I CA CF m)/(MH^2)),-((96 I CA CF m)/(MH^2)),-((176 I CA CF m)/(MH^2)),-((8 I CA CF D m)/(MH^2)),((120 I CA CF m)/(MH^2)),((40 I CA CF m)/(MH^2)),-((4 I CA CF D m)/(MH^2)),-((44 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),-((56 I CA CF m)/(MH^2)),-((4 I CA CF D m)/(MH^2)),-((48 I CA CF m)/(MH^2)),-((88 I CA CF m)/(MH^2)),-((6 I CA CF D m)/(MH^2)),((88 I CA CF m)/(MH^2)),((6 I CA CF D m)/(MH^2)),((72 I CA CF m)/(MH^2)),((16 I CA CF D m)/(MH^2)),((24 I CA CF m)/(MH^2)),((24 I CA CF m)/(MH^2)),((24 I CA CF m)/(MH^2)),-((6 I CA CF D m)/(MH^2)),((40 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),((64 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((60 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((120 I CA CF m)/(MH^2)),-((12 I CA CF D m)/(MH^2)),((40 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),((72 I CA CF m)/(MH^2)),-((40 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),((44 I CA CF m)/(MH^2)),-((4 I CA CF D m)/(MH^2)),((80 I CA CF m)/(MH^2)),-((8 I CA CF D m)/(MH^2)),((48 I CA CF m)/(MH^2)),((96 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((96 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((104 I CA CF m)/(MH^2)),-((24 I CA CF m)/(MH^2)),-((24 I CA CF m)/(MH^2)),-((24 I CA CF m)/(MH^2)),((6 I CA CF D m)/(MH^2)),-((64 I CA CF m)/(MH^2)),((8 I CA CF D m)/(MH^2)),-((72 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),((68 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),((160 I CA CF m)/(MH^2)),-((8 I CA CF D m)/(MH^2)),-((48 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((12 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((24 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((12 I CA CF m)/(MH^2)),-((32 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),((40 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),((40 I CA CF m)/(MH^2)),-((4 I CA CF D m)/(MH^2)),((4 I CA CF m)/(MH^2)),((8 I CA CF m)/(MH^2)),((8 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),((12 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),((32 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),((12 I CA CF m)/(MH^2)),((48 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((52 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((80 I CA CF m)/(MH^2)),((6 I CA CF D m)/(MH^2)),-((4 I CA CF m)/(MH^2)),-((8 I CA CF m)/(MH^2)),-((8 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((8 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((16 I CA CF m)/(MH^2)),((12 I CA CF m)/(MH^2)),((48 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),-((8 I CA CF m)/(MH^2)),-((40 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((48 I CA CF m)/(MH^2)),((48 I CA CF m)/(MH^2)),((88 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),-((64 I CA CF m)/(MH^2)),((2 I CA CF D m)/(MH^2)),-((24 I CA CF m)/(MH^2)),-((72 I CA CF m)/(MH^2)),-((48 I CA CF m)/(MH^2)),((6 I CA CF D m)/(MH^2)),-((48 I CA CF m)/(MH^2)),((48 I CA CF m)/(MH^2)),((88 I CA CF m)/(MH^2)),((4 I CA CF D m)/(MH^2)),-((56 I CA CF m)/(MH^2)),-((2 I CA CF D m)/(MH^2)),((24 I CA CF m)/(MH^2)),-10 I CA CF m (MH^2),3 I CA CF D m (MH^2),-36 I CA CF m (MH^2),8 I CA CF D m (MH^2),6 I CA CF m (MH^2),-3 I CA CF D m (MH^2),6 I CA CF m (MH^2),-I CA CF D m (MH^2),-2 I CA CF m (MH^2),I CA CF D m (MH^2),20 I CA CF m (MH^2),-4 I CA CF D m (MH^2),4 I CA CF m (MH^2)};

Get amplitude expression in terms of Master Integrals

tmp=listplan*coefplan;
amplplan=0;

Do[amplplan=amplplan+tmp[[i]],{i,1,Length[tmp]}]

amplplan//StandardForm

amplplan=IBPReduce[amplplan]/(I CF m)/.MH->mH//Simplify;
amplplan//StandardForm

tmp=listnonplan*coefnonplan;
amplnonplan=0;

Do[amplnonplan=amplnonplan+tmp[[i]],{i,1,Length[tmp]}]

amplnonplan=IBPReduce[amplnonplan]/(I CF m)/.MH->mH//Simplify;
amplnonplan//StandardForm

amplfull=amplplan+amplnonplan;

amplfull//Expand//Variables//StandardForm

Ds[plan]
Ds[nonplan]

Note that in fact only 4 MIs are independent: j[nonplan,0,0,1,1,0,1,0], j[nonplan,0,1,1,0,1,0,1], j[nonplan,1,1,1,1,0,1,1], j[plan,0,0,1,1,1,1,0]. The one with the planar topology here is trivial because it factorises to j[plan,0,0,1,1,1,1,0]=(((∫dk (1/((((k+(Subscript[p, 1])))^2)(((k-(Subscript[p, 2])))^2)))))^2). The others can be found through https://loopedia.mpp.mpg.de/ and map onto the following categories: 
 j[nonplan,0,0,1,1,0,1,0] ⟶ 
j[nonplan,0,1,1,0,1,0,1] ⟶ 
j[nonplan,1,1,1,1,0,1,1] ⟶ 
If the MIs are not known from literature, a good idea is to set up a system of differential equations in the invariants and use existing Feynman integrals as boundary conditions, e.g. I(a,b,c)=∫dk ∫dl (1/(((((k^2)-(m^2)))^a)((((l^2)-(m^2)))^b)((((((k+l+p))^2)-(m^2)))^c))), (d/(dm^2))I(1,1,1)=I(2,1,1)+I(1,2,1)+I(1,1,2) which could be further reduced using the already generated IBP relations. The massless case I(1,1,1)(Subscript[|, (m^2)=0]) which is known from the literature then serves as a boundary condition.

Solving the Master Integrals

MakeDSystem[{j[nonplan,0,0,1,1,0,1,0],j[nonplan,0,1,1,0,1,0,1],j[nonplan,1,1,1,1,0,1,1]},{mH}]/.d->4-2ϵ//MatrixForm//Simplify

DSolve[M1'[mH]==((2-4ϵ)/mH)M1[mH],M1,mH]//StandardForm

Masters={d->4-2ϵ,D->4-2ϵ,j[nonplan,1,1,1,1,0,1,1]->Exp[2 ϵ EulerGamma](-mH^2)^(-2)(((-mH^2)/(μ^2)))^(-2ϵ)(1/(Gamma[1-ϵ]^2))(((-1)/(ϵ^4))+5((π^2)/6)(1/(ϵ^2))+27((Zeta[2])/ϵ)+23((π^4)/36)+(117Zeta[5]-8π^2Zeta[3])ϵ+((19/315)π^6-267Zeta[3]^2)ϵ^2),j[nonplan,0,0,1,1,0,1,0]->Exp[2ϵ EulerGamma](-mH^2)^(1)(((-mH^2)/(μ^2)))^(-2ϵ)((Gamma[1+2ϵ]Gamma[1-ϵ]^3)/(Gamma[3-3ϵ]))*((-1)/(2(ϵ(1-2ϵ)))),j[nonplan,0,1,1,0,1,0,1]->Exp[2 ϵ EulerGamma](((-mH^2)/(μ^2)))^(-2ϵ)((Gamma[1-2ϵ]Gamma[1+ϵ]Gamma[1-ϵ]^2Gamma[1+2ϵ])/(Gamma[2-3ϵ]))(1/(2ϵ^2(1-2ϵ))),j[plan,0,1,1,1,0,0,1]->Exp[2 ϵ EulerGamma](((-mH^2)/(μ^2)))^(-2ϵ)((Gamma[1-2ϵ]Gamma[1+ϵ]Gamma[1-ϵ]^2Gamma[1+2ϵ])/(Gamma[2-3ϵ]))(1/(2ϵ^2(1-2ϵ))),j[plan,0,0,0,1,1,0,1]->Exp[2ϵ EulerGamma](-mH^2)^(1)(((-mH^2)/(μ^2)))^(-2ϵ)((Gamma[1+2ϵ]Gamma[1-ϵ]^3)/(Gamma[3-3ϵ]))*((-1)/(2(ϵ(1-2ϵ)))),j[plan,0,0,1,1,1,1,0]->Exp[2ϵ EulerGamma](((-mH^2)/(μ^2)))^(-2ϵ)Gamma[ϵ]^2((Gamma[1-ϵ]^4)/(Gamma[2-2ϵ]^2))};

amplfull/.Masters//Series[#,{ϵ,0,0}]&//FullSimplify//StandardForm