Photon polarization sum prescription in $e^-e^+\to{}2\gamma$

Question

In calculating the amplitude for the process $e^-\gamma\to{}e^-\gamma$ the substitution $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ is useful to sum over photon polarizations.

If we instead consider the process $e^-e^+\to{}2\gamma$ our amplitude will be of the form $M=\epsilon^*_{\mu}\epsilon^*_{\nu}M^{\mu\nu}$. Is the prescription $\sum\epsilon^*_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ still valid? In case it is not, is there a similar expression to carry out the photon polarization sum and how would this formula be justified?

Answer 1

I just realized that the answer is just stupid. In the case of two outgoing photons when computing $M^*$ you get the epsilons (not complex conjugated) that in the full $|M|^2$ will allow you to use $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$