  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.
