Radiative seesaw model with baryon number violation and upper limit on neutron-antineutron transition time

The minimal scotogenic model where small neutrino masses arise via radiative seesaw, is known to provide a unified framework for neutrino mass and origin of matter via leptogenesis. However if the inflation reheat temperature of the universe is below the sphaleron decoupling temperature, then leptogenesis fails and one way to understand the origin of matter would be to add an effective interaction involving the right-handed neutrino (RHN) N of the form 1 Λ 2 N u R d R d R . This model can lead to observable neutron-antineutron ( n − n ¯ ) oscillation if N is a Majorana fermion. We show that if RHNs are produced nonthermally, we can get a cosmological upper limit on the transition time τ n − n ¯ , which is within the reach of the planned European spallation source high-intensity baryon extraction and measurement/neutron-antineutron experiment. Proton stability is guaranteed by the Z 2 invariance, which prevents the appearance of the Dirac mass term for the neutrino.