Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetries

TL;DR

This paper demonstrates that quark and lepton mixing angles can be derived from SU(2) horizontal symmetries related to weak neutral currents, predicting specific values for neutrino mixing angles consistent with experimental bounds.

Contribution

It introduces a model linking mixing angles to SU(2) horizontal symmetries, providing explicit predictions for neutrino mixing angles that align with experimental constraints.

Findings

Quark mixing angles are determined by SU(2) horizontal symmetries.

Neutrino mixing pattern shows maximal theta_{23} and a specific relation for theta_{12}.

Predicted values for theta_{13} satisfy the experimental bound sin^2(theta_{13})  0.1.

Abstract

We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing angles; on the other hand, a neutrino-like pattern in which theta_{23} is maximal and tan (2 theta_{12}) = 2. The latter turns out to exactly satisfy the ``quark-lepton complementarity condition'' theta_c + theta_{12} = pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise, which satisfy the bound sin^2(theta_{13}) \leq 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717.