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

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.

28 pages, 3 figures, references added, published version

References in corpus (10)

• Observation of electron-antineutrino disappearance at Daya Bay
• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Higgs $\to \mu \tau$ in Abelian and Non-Abelian Flavor Symmetry Models
• Lepton Flavour Violation in Models with A4 Flavour Symmetry
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• A_4 model for the quark mass matrices
• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• Compatibility of theta13 and the Type I Seesaw Model with A4 Symmetry
• An A4 x Z4 model for neutrino mixing

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• Exploring the feasibility of the charged lepton flavor violating decay $\mu \to e+\gamma$ in inverse and linear seesaw mechanisms with $A_4$ flavour symmetry
• The common origin of the family mass hierarchy and CP violation from flavour-dependent vacuum for quarks and leptons