Issue: simplifying chiral splittings in counterterms

[manuel-morales-a]

Hello,

I want to calculate a one-loop amplitude in QED: the self energy of the electron (which you can check here).

First, I generate the amplitudes in FeynArts (using the SM.mod model which, for specific reasons, I cannot change). This model is chiraI. I obtain the amplitudes coming from the (renormalised) theory and the counterterms, and apply some substitution rules (I want the same field renormalisation coefficients for left- and right-handed particles, to reproduce the $Z_{\psi}$ in the example above).

Then, I use FCFAConvert on this amplitude to take it to FeynCalc, and I request UndoChiralSplittings -> True. The chiral splitting is indeed undone in the part of the amplitude that comes from the renormalised theory, but not in the part that comes from the counterterms. So, terms that should have been simplified by using $P_R + P_L = 1$ remain separate, like the first 2 terms in the expression of the image above. dZfL1[2, 1, 1] is simply a counterterm).

One way to reproduce this behaviour is with

expr = (-DiracGamma[Momentum[p, D], D]) . (1 + DiracGamma[5])/2 *dZ + (-DiracGamma[Momentum[p, D], D]) . (1 -DiracGamma[5])/2 * dZ

Simplify[expr]

where no simplification apart from factoring out the 1/2 * dZ happens. If I factor out (-DiracGamma[Momentum[p, D], D]) by hand from the expression above and then Simplify, it does work. However, for the actual case I have to study this becomes unfeasible.

Is there any way to fix this, and make the simplification happen? Apologies in advance if there was something in the documentation, but I looked and I could't find anything that worked for me.

Thanks. Best wishes,

Manuel

[manuel-morales-a]

Apparently, asking FeynCalc to first expand and then simplify does the trick. This means that Simplify[DotExpand[expr]] works, at least in this simplified case.

As an additional comment, it seems that, If expr is written explicitly in terms of GA[6] and GA[7], one needs to substitute them first for their respective definitions in terms of GA[5] for the simplification to work. This means that if

exprG6 = (-DiracGamma[Momentum[p, D], D]) . GA[6]* dZ + (-DiracGamma[Momentum[p, D], D]) . GA[7]*dZ

then Simplify[DotExpand[exprG6]] does not simplify the expression at its fullest, but Simplify[DotExpand[DiracSubstitute67[exprG6]]] does.

I think this solves the issue I described above