Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes

TL;DR

This paper explores how flavons in discrete flavour symmetry models induce lepton flavour violation processes, linking these processes to lepton mixing patterns, with detailed calculations in an $A_4$ symmetry framework.

Contribution

It provides a detailed analysis of flavon-induced lepton flavour violation in $A_4$ models, including decay rate calculations and sum rules, highlighting the connection to lepton mixing and the role of flavon representations.

Findings

Certain LFV decay processes are allowed by residual $Z_3$ symmetry.

Decay rates depend on flavon representation (pseudo-real or complex).

Current constraints permit flavon masses around hundreds of GeV.

Abstract

In leptonic flavour models with discrete flavour symmetries, couplings between flavons and leptons can result in special flavour structures after they gain vacuum expectation values. At the same time, they can also contribute to the other lepton-flavour-violating processes. We study the flavon-induced LFV 3-body charged lepton decays and radiative decays and we take as example the $A_4$ discrete symmetry. In $A_4$ models, a $Z_3$ residual symmetry roughly holds in the charged lepton sector for the realisation of tri-bimaximal mixing at leading order. The only processes allowed by this symmetry are $\tau^-\to \mu^+ e^- e^-, e^+ \mu^- \mu^-$, and the other 3-body and all radiative decays are suppressed by small $Z_3$-breaking effects. These processes also depend on the representation the flavon is in, whether pseudo-real (case i) or complex (case ii). We calculate the decay rates for all processes for each case and derive their strong connection with lepton flavour mixing. In case i, sum rules for the branching ratios of these processes are obtained, with typical examples $\text{Br}(\tau^-\to \mu^+ e^- e^-) \approx \text{Br}(\tau^-\to e^+ \mu^- \mu^-)$ and $\text{Br}(\tau^-\to e^- \gamma) \approx \text{Br}(\tau^-\to \mu^- \gamma)$. In case ii, we observe that the mixing between two $Z_3$-covariant flavons plays an important role. All processes are suppressed by charged lepton masses and current experimental constraints allow the electroweak scale and the flavon masses to be around hundreds of GeV. Our discussion can be generalised in other flavour models with different flavour symmetries.