This Notebook intends to show the use of TID (Tensor Integral Decomposition) instead of OneLoop. This is because OneLoop has problems sometimes. Working with TID one has to be careful with the dimension D

This Version is compatible with FeynCalc 10.1.0
Version of 09/12/2024
Author; Jorge C. Romão
email: jorge.romao@tecnico.ulisboa.pt

<<FeynCalc`

The amplitude

SetOptions[PaVeReduce,A0ToB0->True];

(*Now write the numerator of the Feynman diagram.We define the constant 
C=-alpha/(4 pi) 
The minus sign comes from the photon propagator.The factor i/(16 pi^2) is already included in this definition
*)

(*Everything has to be in dimension D*)num:=C GAD[mu].(GSD[p]+GSD[k]+m).GAD[mu]//Contract
(*Define the amplitude*)
amp:=num*FAD[{p+k,m},{k}]

(*Calculate the result. The minus sign comes from the fact that
- i\Sigma=diagram
*)

ans1= -(-I/Pi^2) TID[amp,k,UsePaVeBasis-> True,ToPaVe->True]//Simplify

ans2=ans1/. A0[x_]-> x(B0[0,x,x]+1)//Simplify

The D=4 part. Note that D is explicit but also implicit in the momenta and DiracGamma in D dimensions. This is why I Use //FCI /. D-> 4

ansD4=(((ans2 /.D-> 4)//FCI)/.D->4)//FCE

ansDiv=Coefficient[ans2/. {B0[x_,y_,z_]-> 2/eps,PaVe[0,{x_},{y_,z_}]-> 2/eps},eps,-1]/eps

ansFinite=(((Coefficient[(ansDiv//FCE)/.D-> 4-eps//Expand,eps,0])//FCI)/.D->4)

Final=(ansD4+ansFinite)//FCE//Simplify

Calculate delta m

A=Coefficient[Final,GS[p],0];

B=Coefficient[Final,GS[p],1];

delm=((AN+m BN)//FCE)/.SP[p,p]->m^2//Simplify

Calculate delta Z2

Ap2=A/.SP[p,p]->p2

Bp2=B/.SP[p,p]->p2

aux=2 m D[Ap2,p2]+Bp2+2 m^2 D[Bp2,p2]/.D[B0[p2,0,m^2],p2]->DB0[p2,0,m^2]

aux2=aux/.p2->m^2

delZ2=Simplify[aux2]