Universal Seesaw Pati-Salam Model with P for Strong CP

We develop a universal seesaw version of the Pati-Salam model wherein quarks and leptons of each family are unified into common multiplets transforming as $\{\psi_L(2,1,4)+ \psi_R(1,2,4)\}$ under the $SU(2)_L \times SU(2)_R \times SU(4)_c$ gauge symmetry. Parity symmetry is spontaneously broken in the model, which helps in solving the strong CP problem without the axion. The Higgs sector of the model is very simple, consisting of a single pair of $\{H_L(2,1,4)+ H_R(1,2,4)\}$ fields. Fermion masses arise through mixing of the chiral fermions with vector-like quarks and leptons contained in $(1,1,15)$ as well as $\{(1,1,10)_L+(1,1,10)_R\}$ multiplets via a universal seesaw mechanism. Consistency of such a spectrum with the observed quark and lepton masses is established. The parity solution to the strong CP problem is shown to be effective in this framework, although there are new loop contributions to $\bar{\theta}$, compared to the analogous left-right symmetric model, arising from color sextet and octet fermions, as well as from diagrams mediated by leptoquark bosons. We also find that, in this setup, although lepton number is broken, neutrino masses remain zero at the tree-level. Small and finite Majorana neutrino masses are induced via one-loop diagrams, which we analyze and show to be compatible with oscillation experiments.