Testing Seesaw and Leptogenesis via Gravitational Waves: Majorana versus Dirac

We investigate the B-L gauge extension of the Standard Model that the Dirac seesaw mechanism with thermal Leptogenesis can be tested using the stochastic gravitational background (SGWB) emanating from a network of cosmic strings when B-L symmetry is broken. With right-handed neutrino mass lighter than the typical scale of grand unification, the B-L symmetry protecting the right-handed neutrinos leads to constraints on the Yukawa couplings for both Dirac and Majorana scenarios. Estimating the predicted gravitational wave background we find that future space-borne missions could probe the range concerning thermal Dirac Leptogenesis. In a comparative analysis between such probes of gravitational wave sourced from cosmic strings in Dirac and Majorana Leptogenesis in the B-L extension, based on the energy scales of the Leptogenesis, for instance, GW detectors will be able to probe the scale of Dirac Leptogenesis upto $ 10^{9}$ GeV, while for Majorana Leptogenesis it would be upto $ 10^{12}$ GeV.