An $S_3$ flavored left-right symmetric model of quarks

TL;DR

This paper develops an $S_3$ symmetric left-right model for quarks, leading to a specific structure of quark masses and mixing, with realistic CKM matrix and first-generation quark mass ratios.

Contribution

It introduces an $S_3$ flavor symmetry into a left-right symmetric model, resulting in a novel quark mass and mixing pattern with minimal Yukawa couplings.

Findings

First two generations mix at leading order

CKM matrix is block diagonal initially

First generation quark masses are consistent with $m_u/m_d$ ratio

Abstract

We construct a model based on the electroweak gauge group $\rm SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ augmented by an $S_3$ symmetry. We assign nontrivial $S_3$ transformation properties to the quarks and consequently we need two scalar bidoublets. Despite the extra bidoublet we have only six Yukawa couplings thanks to the discrete symmetry. Diagonalization of the quark mass matrices shows that at the leading order only the first two generations mix, resulting in a block diagonal CKM matrix, and the first generation quarks are massless. Inclusion of subleading terms produce an acceptable CKM matrix up to corrections of order $\lambda^4$. As for the first generation quark masses, we obtain satisfactory value of $m_u/m_d$. The masses themselves, though being in the same ballpark, turn out to be somewhat smaller than the accepted range.