Complex "squared" amplitude

[AlessioV01]

I am trying to compute the "squared" amplitude for the process $\nu_\mu d \longrightarrow \mu u \gamma$ at tree level for massless quarks. If I specify that the final photon state is transverse with TransversePolarizationVectors -> {p5} when I use FCFAConvert, can I still use the fact that the sum over the polarizations is $-g_{\mu \nu}$? i.e. can I use DoPolarizationSums[ampSquared[0], p5, 0] or do I need to insert the auxiliary vector $n$ instead of $0$? Because my "squared" amplitude is complex if I set it to $0$, but I don't understand why...

Thanks in advance

[vsht]

The TransversePolarizationVectors option only sets whether $\varepsilon(p) \cdot p = 0$ holds for the given polarization vector
$\varepsilon(p)$ or not. The name is indeed somewhat misleading...

For physical photons and gluons I would always DoPolarizationSums with an auxiliary vector. The $-g^{\mu \nu}$-trick is something that doesn't work in every possible situation. However, even when using it where you're not allowed to, this won't make your squared amplitude complex. Here the issue must be elsewhere.