FCMultiLoopTID giving zero

[SumitBanikGit]

Hi,

Is this a bug that FCMultiLoopTID yields zero here?

I believe it is due to the ApartFF[] option, but I could not understand why.

Is there a way to simplify numerator and denominator factors, like, in this case, having common factors?

Best regards,
Sumit

test1 = SPD[l2] FeynAmpDenominator[
   PropagatorDenominator[Momentum[l1, D], 0], 
   PropagatorDenominator[Momentum[l2, D], 0], 
   PropagatorDenominator[Momentum[l2, D], 0], 
   PropagatorDenominator[Momentum[l2, D], 0], 
   PropagatorDenominator[Momentum[l1 + l2, D], 0]]
FCMultiLoopTID[test1, {l1, l2}]

[vsht]

Hi,

this integral is scaleless, so it is zero in dim reg. If you e.g. add a mass to any of the propagators it will not vanish anymore.

Cheers,
Vlad

[SumitBanikGit]

Hi Vlad,

thanks a lot for the answer! Yes, I agree with you. However, I don't get zero if I manually cancel the numerator scalar product with the denominator and use FCMultiLoopTID.

test2 = FeynAmpDenominator[PropagatorDenominator[Momentum[l1, D], 0], 
  PropagatorDenominator[Momentum[l2, D], 0], 
  PropagatorDenominator[Momentum[l2, D], 0], 
  PropagatorDenominator[Momentum[l1 + l2, D], 0]]
FCMultiLoopTID[test2, {l1, l2}]

which is the same as test1 in the original post, but it does not give a zero. Is it a bug?

Best regards,
Sumit

[vsht]

Hi,

it's because FCMultiLoopTID sorts out integrals free of numerators, so
no further simplifications are applied to them. You can use FDS or
FCLoopScalelessQ, though:

FDS[test2, l1, l2]

FCLoopScalelessQ[test2, {l1, l2}]

Cheers,
Vlad