Name: Adrian (email_not_shown)
Date: 10/11/17-04:44:37 PM Z


Dear Vladyslav,

I'm trying to calculate a diagram using three different approaches

1) OneLoop
2) TID -> OneLoop
3) OneLoopSimplify -> OneLoop

The first two give a correct result while the last one does not (Mathematica 11.1 and the latest stable version of FeynCalc).

Please note that the difference doesn't seem to be caused by the usual (D-4)/(D-4) terms. I guess that OneLoopSimplify treats chiral projections incorrectly. The example is appended below.

By the way, what is the ``official way" of calculating one-loop integrals, 1,2,3 or maybe none of them?

Best wishes,
Adrian

In[2]:= InfParts := {B0[X__] -> FinB0[X] + 1/eps,
   A0[Y_] -> FinA0[Y] + Y/eps};

R = (1 + GA[5])/2;
L = (1 - GA[5])/2;
fad := FeynAmpDenominator;
pd[q_, m_] := PropagatorDenominator[Momentum[q, D], m];

In[9]:= DiagAnum = -I (SPD[k, k] MTD[mu, nu] -
     FVD[k, mu] FVD[k, nu]) GAD[
     mu].(Fal L + FalCC R).(GSD[k - p] + Mcc L + M R).GAD[
     nu].(Fbe L + FbeCC R);

In[10]:= DiagAden = fad[pd[k - p, mF], pd[k, mV], pd[k, 0]];

In[12]:= DiagA = ((4 Pi)^2/(2 Pi)^4) DiagAnum DiagAden ;

(*First way*)

In[16]:= ResA0 = OneLoop[k, DiagA];

In[17]:= ResA0 = ResA0 // DiracSimplify

In[18]:= ResA0 =
 ResA0 /. InfParts /. D -> 4 - 2 eps // Series[#, {eps, 0, 0}] & //
  Normal

(*Second way*)

In[30]:= ResA = OneLoopSimplify[DiagA, k];

In[20]:= ResA = OneLoop[k, ResA];

In[21]:= ResA = ResA // DiracSimplify;

In[22]:= ResA =
 ResA /. InfParts /. D -> 4 - 2 eps // Series[#, {eps, 0, 0}] & //
  Normal

(*Third way*)

In[23]:= ResA1 = TID[DiagA, k];

In[24]:= ResA1 = OneLoop[k, ResA1];

In[25]:= ResA1 = ResA1 // DiracSimplify;

In[26]:= ResA1 =
 ResA1 /. InfParts /. D -> 4 - 2 eps // Series[#, {eps, 0, 0}] & //
  Normal

(*Comparison*)

In[27]:= ResA1 - ResA0 // Simplify

Out[27]= 0

In[28]:= Limit[eps ( ResA1 - ResA), eps -> 0] // Simplify

Out[28]= -(3/
  2) (FalCC M - Fal Mcc) (Fbe (-1 + DiracGamma[5]) +
   FbeCC (1 + DiracGamma[5]))



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