Hi Vladyslav, Duarte and others,
Recently, I started to receive these emails from this thread, and it took me a while to realize when and why it was happening! It’s nice to see these messages since it’s a convenient way to see what people are working on, and, more importantly, how they employ computer algebra software like FeynCalc for their work. Anyway, I am responding here because I think that I might be able to provide some assistance to folks like Duarte, who I think are interested in quickly obtaining explicit results to one loop integrals with as little hassle as possible.
For this, I would like to offer a rather new Mathematica application, Package-X (packagex.hepforge.org, see also packagex.hepforge.org/primer-2.1.1.pdf), of which I am an author, and which is designed to do just that. Since Package-X is much less elaborate than FeynCalc, its functions are less finicky and there is less setting up. Indeed, each of Duarte’s integrals can be done in one line (see attached), with the explicit result (UV divergent and finite parts) obtained in naive dimensional regularization.
Sure, naive dimensional regularization is inconsistent. But at one-loop order, its inconsistencies affect just a few handful of one loop integrals. And for such integrals (like the VVA triangle), it is easy enough to enforce necessary Ward identities by hand, and I provide a tutorial that explains how to do it, packagex.hepforge.org/Documentation/HTML/X/tutorial/AdlersMethod.html. It think the benefits of its simplicity outweigh the complications brought in by other schemes, at least at one loop order.
Now I emphasize that Package-X is significantly more limited in scope than FeynCalc, especially for higher order calculations. For more involved calculations which makes heavy use of FeynCalc machinery, it is more practical to mainly use FeynCalc, and then to link it to Package-X through FeynHelpers (github.com/FeynCalc/feynhelpers, and also packagex.hepforge.org/Documentation/HTML/X/tutorial/LinkingToFeynCalc.html) to obtain explicit results to one loop integrals.
While I understand that it might not be appropriate to advertise another Mathematica package on this forum, I do think it complements FeynCalc well, and that users like Duarte might find it quite convenient!
Happy computing,
-Hiren Patel
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