Effective Theory for Baryogenesis with a Majorana Fermion Pair Coupled to Quarks

With a goal toward explaining the observed baryon asymmetry of the Universe, we extend the standard model (SM) by adding a vector-vector dimension-six effective operator coupling a new Dirac fermion $\chi$, uncharged under the SM gauge symmetries but charged under baryon number, to a quark-like up-type fermion and two identical down-type fermions. We introduce baryon number violation by adding Majorana masses to $\chi$, which splits the Dirac fermion into two Majorana fermions with unequal masses. We speculate on the origin of the effective operator, the Majorana mass, and the new physics sector connection to the SM, by considering some ultraviolet completion examples. In addition to the baryon number violation, we show that $C$ and $CP$ invariances can be violated in the theory, and the interference between tree and loop amplitudes with on-shell intermediate states can lead to a baryon asymmetry in $\chi$ decay and scattering processes. We write down the Boltzmann equation for baryon number in the early Universe incorporating the decay and scattering baryon asymmetries. We provide numerical estimates for the baryon asymmetry generated, and for the neutron-antineutron oscillation rate.