R-Parity Violation and Family Symmetry

TL;DR

This paper explores how family symmetry, specifically the non-abelian discrete symmetry Q_6, constrains R-parity violating operators and predicts fixed ratios of lepton flavor violating decay rates.

Contribution

It introduces a concrete model with Q_6 symmetry that limits RPV operators and predicts specific ratios of lepton flavor violating decay rates.

Findings

Ratios of decay rates for tau to 3e and tau to 3mu are fixed by family symmetry.

The model includes only three RPV trilinear operators with no baryon number violation.

Predicted BR(tau to 3e)/BR(tau to 3mu) ~ 4 m_mu^2/m_tau^2.

Abstract

In this talk, we investigate the implications of R-parity violating (RPV) operators in a model with family symmetry. Family symmetry can determine the form of RPV operators as well as the Yukawa matrices. We consider a concrete model with non-abelian discrete symmetry Q_6, which has only three RPV trilinear operators with no baryon number violating terms. We find that ratios of decay rates of the lepton flavor violating processes are fixed thanks to the family symmetry, predicting BR(tau to 3e)/BR(tau to 3mu) ~ 4 m_{mu}^2/m_{tau}^2.