Name: V. Shtabovenko (email_not_shown)
Date: 01/31/18-10:05:21 AM Z


Hi,

well, as you surely know, in the conventional DR *all* scaleless
integrals are put to zero, regardless of whether they are scaleless
because the divergence is only polynomial or for other reasons. Since it
is customary to regulate both UV and IR singularities with the same
regulator (unless an additional IR regulator is introduced), in
integrals B0(0,0,0) you essentially get 1/eps_UV - 1/eps_IR = 0.

Having said that, one should mention that at least at 1-loop one could
distinguish between UV and IR singularities, although this is quite
painful to implement. Package-X can do this and I also implemented an
experimental option (c.f. p. 18 in 1611.06793 ) to have this feature in
FeynCalc, although I have not tested it too much.

It is a nice thing for illustration/educational purposes, but is not
really needed in real-life calculations. Otherwise, the whole idea of
DR would not make any sense. Moreover, as soon as IBP reduction comes
into play, the UV and IR poles will still get mixed up even at 1-loop.
In practice, if one really needs to disentangle UV and IR poles, one
would just use a different regulator for IR (e.g. fictitious masses).

Cheers,
Vladyslav

Am 30.01.2018 um 18:34 schrieb Duarte:
> Dear Vladyslav,
>
> thank you so much for all the help.
>
> I come to you now with another question. Feyncalc thinks that B0(0,0,0)
> is zero (where B0 is the Passarino-Veltman usual function). But the
> truth is that B0(0,0,0) is doubly divergent: infrared (because we have
> ln 0) and UV (because of the 1/\epsilon divergence).
>
> So what's happening here? How come does Feyncalc think B0(0,0,0)=0?
>
> Best regards,
> Duarte
>



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