Lepton masses, mixings and FCNC in a minimal S_3-invariant extension of the Standard Model

TL;DR

This paper reparametrizes lepton mass matrices within a minimal S_3-invariant Standard Model extension, deriving analytical expressions for neutrino mixing parameters and FCNC process rates, showing strong suppression consistent with experimental bounds.

Contribution

It provides explicit analytical formulas for neutrino mixing angles, phases, and FCNC rates in an S_3-invariant model, highlighting the suppression of flavor-changing processes.

Findings

Neutrino mixing matrix closely matches tri-bimaximal form.

FCNC processes are suppressed below experimental limits.

Analytical expressions relate masses to mixing angles and FCNC rates.

Abstract

The mass matrices of the charged leptons and neutrinos, previously derived in a minimal S_3-invariant extension of the Standard Model, were reparametrized in terms of their eigenvalues. We obtained explicit, analytical expressions for all entries in the neutrino mixing matrix, V_PMNS, the neutrino mixing angles and the Majorana phases as functions of the masses of charged leptons and neutrinos in excellent agreement with the latest experimental values. The resulting V_PMNS matrix is very close to the tri-bimaximal form of the neutrino mixing matrix. We also derived explicit analytical expressions for the matrices of the Yukawa couplings and computed the branching ratios of some selected flavour changing neutral current processes 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.