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I'm currently doing some one-loop calculations for some bad-*** decays with vector final states, which yield me some tri-tensor threepoint functions. I know the Passarino-Veltmann reduction scheme, and also got the general reduction formulas from Denner-Dietmeier to simplify expressions with a general number of external tensor indices into fundamental loop integrals. But I still have some questions:

Do I understand correctly, that the form factors in front of external 4-momenta involving different external tensor indices but the same # of external momenta (e.g. 2 x p1, 1 x p2 in the tri-tensor 3-point case, or just p1 p2 in the di-tensor 3-point case, when p1,p2 denote the external momenta) they have the same FF? So when Denner and Dietmeier state me several solutions for different combinations of these external momenta I can only pick one of these? (like one can do in the di-tensor 3-point case?)

Second: Denner and Dietmeier's solution give raise to additional factors proportional to m_0,1,2 square. When I calculated the self-energy correction of my external vector particle these contributions canceled each other so I only got a final expression involving only loop-integrals for my virtual diagram. But when I do the same for an internal photon loop from e.g. a fermionic final state to my vector final state this seems not to be the case. I didn't integrate my matrix elements numerically yet, but should this worry me?

Thirds: do you know any software that can help me verify my calculations? I played around a bit with some mathematica modules but never was really satisfied.

Thanks a lot,

Florian

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# QED loop calculations.

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