Fermion Masses and Mixings, Leptogenesis and Baryon Number Violation in Pati-Salam Model

In this work we study a predictive model based on a partially unified theory possessing the gauge symmetry of the Pati-Salam group, $SU(2)_L\times SU(2)_R\times SU(4)_C$ supplemented by a global Peccei-Quinn symmetry, $U(1)_{PQ}$. A comprehensive analysis of the Higgs potential is carried out in a minimal set-up. The assumed Peccei-Quinn symmetry along with solving the strong CP problem, can provide axion as the dark matter candidate. This minimal set-up with limited number of Yukawa parameters can successfully incorporate the hierarchies in the charged fermion masses and mixings. The automatic existence of the heavy Majorana neutrinos generate the extremely small light neutrino masses through the seesaw mechanism, which is also responsible for producing the observed cosmological matter-antimatter asymmetry of the universe. We find interesting correlation between the low scale neutrino observables and the baryon asymmetry in this model. Baryon number violating nucleon decay processes mediated by the scalar diquarks and leptoquarks in this framework are found to be, $n,p\to \ell+m, \ell^c + m$ ($m=$ meson, $\ell=$ lepton, $\ell^c=$ antilepton) and $n,p\to \ell+\ell^c + \ell^c$. For some choice of the parameters of the theory, these decay rates can be within the observable range. Another baryon number violating process, the neutron-antineutron oscillation can also be in the observable range.