Can CP-violation arise due to interference between two tree-level diagrams in a QFT?

Question

In Leptogenesis, CP-asymetry arises due to the interference of the tree-level amplitude $N\rightarrow l_\alpha\phi$ (where $N$ is heavy sterile neutrino, $l_\alpha$ is a lepton flavour, and $\phi$ is the Higgs) with the higher order amplitudes (say, one-loop amplitude).

This was a decay. Let us consider an scattering so that there may me more than one diagrams at the tree level. For a given scattering $A+B\rightarrow C+D$, there may be two tree-level diagrams. Similarly for the process $\bar{A}+\bar{B}\rightarrow \bar{C}+\bar{D}$ where will be two again. Can we have CP-asymetry due to the interference between two different tree-level scattering amplitudes?

I believe the question makes sense. If not I shall try to clarify it further.

Answer 1

Generating CP asymmetry from scattering process is indeed possible. Actually, already in leptogenesis people have considered such processes because they dominate at high energy ($T>M_N$) but it turns out that they have negligible effects on the final asymmetry (e.g., hep-ph/0309342).

A field $\psi$, which has CP violating interactions with fermions $f$, can lead to different rates for the processes $\psi\psi\to \bar f$ and $\overline{\psi\psi}\to f$ provided departure from thermal (c.f. 1407.4566 and refs therein).