S_3-flavour symmetry as realized in lepton flavour violating processes

TL;DR

This paper explores how an S_3-flavour symmetry influences lepton flavour violating processes, deriving analytical expressions and showing that the symmetry suppresses FCNC processes below experimental bounds, with a small but notable effect on the muon's magnetic moment anomaly.

Contribution

It provides explicit analytical formulas within an S_3-invariant Standard Model extension and assesses their impact on lepton flavour violation and muon magnetic moment anomaly.

Findings

FCNC processes are suppressed below experimental limits by the S_3 x Z_2 symmetry.

The symmetry's effect on muon magnetic moment is small but non-negligible.

Analytical expressions for Yukawa matrices are derived in the S_3 framework.

Abstract

A variety of lepton flavour violating effects related to the recent discovery of neutrino oscillations and mixings is here systematically discussed in terms of an S_3-flavour permutational symmetry. After a brief review of some relevant results on lepton masses and mixings, that had been derived in the framework of a Minimal S_3-Invariant Extension of the Standard Model, we derive explicit analytical expressions for the matrices of the Yukawa couplings and compute the branching ratios of some selected flavour changing neutral current (FCNC) processes, as well as, the contribution of the exchange of neutral flavour changing scalars to the anomaly of the muon's magnetic moment as functions of the masses of the charged leptons and the neutral Higgs bosons. We find that the S_3 x Z_2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector well below the present experimental upper bounds by many orders of magnitude. The contribution of FCNC to the anomaly of the muon's magnetic moment is small but non-negligible.