Mass Limit for Light Flavon with Residual $Z_3$ Symmetry

TL;DR

This paper proposes a modified $A_4$ flavor model with a residual $Z_3$ symmetry, predicting a light flavon with a mass limit of 60 GeV and potential detection at the LHC through specific tau decay modes.

Contribution

It introduces a new $A_4$ flavon with residual $Z_3$ symmetry, analyzing its mass constraints and collider signatures, extending previous flavor models with novel phenomenological predictions.

Findings

Flavon mass limit of 60 GeV from tau decay modes.

Predicted ratio of branching ratios for specific tau decays.

Potential flavon detection at the LHC with a cross section of about 1 fb.

Abstract

We present a modified Altarelli and Feruglio $A_4$ model where an additional $A_4$ singlet-prime flavon is introduced. In this model, non-zero $\theta _{13}$ is given by this additional $A_4$ singlet-prime flavon which breaks tri-bimaximal mixing. In the framework of the supersymmetry with $U(1)_R$ symmetry, we obtain vacuum expectation values (VEVs) and VEV alignments of flavons through driving fields. It is considered that flavon induces distinctive flavor violating process if flavon mass is light. Assuming mass of SUSY particles are sufficiently heavy so that the SUSY contributions can be negligible, we discuss the flavor violating Yukawa interaction through flavon exchange in the charged lepton sector. According to the potential analysis, the VEV of flavon breaks $A_4$ down to $Z_3$ in the charged lepton sector and relation among flavon masses is determined. Thanks for the residual $Z_3$ symmetry, many lepton flavor violating decay modes are forbidden except for $\tau \rightarrow \mu \mu \bar{e}$ and $\tau \rightarrow e e \bar{\mu}$. A mass limit of the flavon from these three-body decay modes is $60$~GeV taking into account the current experimental lower bounds at the Belle experiment. In our model, we predict a ratio of the branching ratios $\tau \rightarrow \mu \mu \bar{e}$ and $\tau \rightarrow e e \bar{\mu}$ by using known charged lepton masses. We also find that the production cross section for the flavon can be $\mathcal{O}(1)$ fb. Thus the flavon would be found at the LHC run 2 by searching for 4-tau lepton signal.