Radiative Mass Mechanism: Addressing the Flavour Hierarchy and Strong CP Puzzle

We propose a class of models based on the parity invariant Left-Right Symmetric Model (LRSM), which incorporates the mechanism of radiative generation of fermion masses while simultaneously possessing the solution to the Strong CP problem. A flavour non-universal gauged abelian symmetry is imposed on top of LRSM, which helps in inducing the masses of second and first-generation fermions at one-loop and two-loop, respectively, and thereby reproduces the hierarchical spectrum of the masses. Parity invariance requires the vanishing of the strong CP parameter at the zeroth order, and the non-zero contribution arises at the two-loop level, which is in agreement with the experimental constraints. The minimal model predicts flavour symmetry breaking scale and the $SU(2)_R$ symmetry breaking scale at the same level. flavour non-universality of the new gauge interaction leads to various flavour-changing transitions both in quarks and leptonic sectors and, therefore, has various phenomenologically interesting signatures. The model predicts a new physics scale near $10^8$ GeV or above for phenomenological consistent solutions. This, in turn, restricts strong CP phase $\bar{\theta} \lesssim 10^{-14}$ as the parity breaking scale and flavour scale are related in the minimal framework.