Baryon Asymmetry from the Decay and Scattering of a Majorana Fermion Pair Coupled to Quarks

We compute the baryon asymmetry in decay and scattering processes involving the electromagnetically charge-neutral fermion $\chi$ that carries nonzero baryon number and interacts with quark-like fermions $U,D$ via a vector-vector dimension-six effective operator, in the theory we developed in our earlier work. Majorana masses for the $\chi$ break baryon number and split the Dirac fermion $\chi$ into a pair of Majorana fermions $X_n$ with indefinite baryon number. We identify loop amplitudes for $X_n$ decay and scattering processes that are sensitive to the baryon number violation. The phases in the Majorana mass and couplings, in conjunction with the phase from intermediate onshell states, lead to $C$ and $CP$ violation in these processes. For some representative parameter choices, we numerically compute the decay and scattering baryon asymmetries between the process and its conjugate process, and find that the asymmetry generated is very interesting for explaining the baryon asymmetry of the Universe.