Name: Vladyslav Shtabovenko (email_not_shown)
Date: 12/25/16-07:35:54 PM Z

This one seems to be the oldest question (16 years old) on this mailing list without a satisfying answer.

I checked the integral with the current dev version and FeynHelpers and agree with the OneLoopFPI output
up to the relative sign in front of the 4:

<< FeynCalc`

SP[p, p] = pp;
int = 1/(I Pi^2) FAD[{p - k}, {k, mW}] GSD[k];
res1 = OneLoop[k, int]
(PaXEvaluate[16 Pi^4 res1, PaXImplicitPrefactor -> 1/(2 Pi)^D,
PaXSeries -> {{pp, 0, 0}}] /. {ScaleMu^2 ->
ScaleMu^2 E^EulerGamma/(4 Pi),
1/Epsilon -> 2/Epsilon}) // Simplify

One should also mention that it is very easy to make a mistake here, if one just naively
puts p^2 to zero in B0:

(PaXEvaluate[
16 Pi^4 res1 /. B0[FCI@SP[p, p], 0, mW^2] -> B0[0, 0, mW^2],
PaXImplicitPrefactor -> 1/(2 Pi)^D,
PaXSeries -> {{pp, 0, 1}}] /. {ScaleMu^2 ->
ScaleMu^2 E^EulerGamma/(4 Pi),
1/Epsilon -> 2/Epsilon}) // Simplify

This is because B0 is multiplied by 1/p^2, so one would loose a finite contribution when doing so.
I guess this is what might have happened to OP.

Cheers,

> Dear Rolf Mertig Professor:
>
> I have calculate some feynman diagrams of elecweak model.Compairing
> large gauge boson mass,the light quark momentum can be neglected,so
> analytic results will be gotten.I expand B0,C0,D0 functions when
> neglecting external momentum.But I found the results achieved by using
> OneLoop function are different from the results achieved by hand.
> So I chosed a very simple loop integration to check my results,and find
> maybe OneLoop function is wrong.
> I write a small function "OneLoopFPI" to imitate the processes of
> calculations by hand Using feynman parameters method in common.I found
> it give the same results with my previous results gotten by hand.
> I send you a ps file about a very simple question dealing with OneLoop
> and OneLoopFPI function.Maybe you can find where I was wrong.
> Thanks for your attentions.
>
> zhou yong 14,Dec,2000

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