Quark and lepton mixing angles with a dodeca-symmetry

TL;DR

This paper explores how a dodeca-symmetry at the electroweak scale can determine quark and lepton mixing angles, proposing a specific symmetry-based framework that predicts mixing angles and addresses the strong CP problem.

Contribution

It introduces a novel application of D_12 symmetry to fix mixing angles and discusses symmetry breaking and implications for the strong CP problem.

Findings

Predicts theta_C = 15° at leading order

Relates solar neutrino angle to the Cabibbo angle as theta_sol + theta_C ~ 45°

Suggests a small symmetry breaking can adjust theta_C to observed values

Abstract

The discrete symmetry D_12 at the electroweak scale is used to fix the quark and lepton mixing angles. At the leading order, the Cabbibo angle theta_C is 15^o, and the PMNS matrix is of a bi-dodeca-mixing form giving the Solar-neutrino angle theta_sol=30^o. Thus, there results the relation theta_sol+theta_C ~ 45^o. Out of discrete vacua, a certain vacuum is chosen for this assignment to be consistent with the dodeca-symmetry. A shift of theta_C from 15^o to 13.14^o might arise from a small breaking of the dodeca-symmetry. The spontaneous breaking leading to the required electroweak vacuum is made possible by introducing an additional parity in an effective field approach or by realizing the electroweak dodeca-symmetry explicitly at a high energy scale. At the vacuum we chose Arg.Det.M_q is nonzero, and hence a solution of the strong CP problem invites a very light axion at a high energy scale. We also comment how the next level corrections can fit the mixing angles to the observed values.