Name: Vladyslav Shtabovenko (email_not_shown)
Date: 06/01/16-01:07:10 PM Z


Hi,

Am 01.06.2016 um 11:51 schrieb Steffen Schwertfeger:
> Dear all,
>
> On 01/06/16 11:43, Vladyslav Shtabovenko wrote:
>> The only way to obtain m^2*B0[0, m^2, m^2] that I currently see would
>> be take the D->4 limit via
>>
>> res2/.D->4
>
> which is exactly what I did. Is there a way to properly take the limit?

in general, to be able to take the limit correctly you need to know the
coefficient of the 1/Epsilon_UV pole of the PaVe function. Those are
tabulated in the work of Denner et al, c.f. Appendix A of
arXiv:hep-ph/0509141.

Of course, when taking the limit it is always assumed that the PaVe
function is not IR divergent. Which is the case for all A's and B's but
in general not true for C's and D's.

So you could use $LimitTo4=True (which is now safe) to recover the
results that you had in the stable version. One has to keep in mind,
that only some cases for B0, B1, B00 and B11 implemented, so it doesn't
give you a general solution.

Hmm, I guess that for simplifying terms like f(D)*PaVe one could add
a new function that would take the limit for the known cases. Again,
under the assumption that C's and D's are IR finite and f(D) is a
rational function. Let me see how difficult it would be to implement...

Cheers,
Vladyslav

>
> Kind regards,
> Steffen Schwertfeger
>



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