Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix

Lorenzo Calibbi,Oscar Vives,M L López-Ibáñez,Aurora Melis

doi:10.1140/epjc/s10052-021-09741-1

Abstract

The confirmation of the discrepancy with the Standard Model predictions in the anomalous magnetic moment by the Muon g-2 experiment at Fermilab points to a low scale of new physics. Flavour symmetries broken at low energies can account for this discrepancy but these models are much more restricted, as they would also generate off-diagonal entries in the dipole moment matrix. Therefore, if we assume that the observed discrepancy in the muon g-2 is explained by the contributions of a low-energy flavor symmetry, lepton flavour violating processes can constrain the structure of the lepton mass matrices and therefore the flavour symmetries themselves predicting these structures. We apply these ideas to several discrete flavour symmetries popular in the leptonic sector, such as Delta (27), A_4, and A_5 < imes mathrm{CP}.

Highlights

The new results from the Muon g-2 experiment at Fermilab [1] have confirmed the long-standing discrepancy between the Standard Model (SM) prediction for the anomalous magnetic moment of the muon, aμ =/2, and the previous BNL measurements [2,3]
If we assume that the observed discrepancy in the muon g − 2 is explained by the contributions of a low-energy flavor symmetry, lepton flavour violating processes can constrain the structure of the lepton mass matrices and the flavour symmetries themselves predicting these structures
We will analyse several popular flavour symmetries in neutrino physics to see if they can be responsible of the observed discrepancy in the anomalous magnetic moment of the muon while, at the same time satisfying the bounds on lepton flavour violating (LFV) processes that we translated in the constraints shown in Eq (22)

Summary

Introduction

The central value of the measured discrepancy in Eq (1) is roughly a factor 1.5 larger This implies that a new physics contribution with no special enhancement factor, couplings of electroweak size, and proportional to the muon mass would point to a mass scale of only 65 GeV!! Or even the new physics responsible for the new contributions to dipole moments is the very same flavour dynamics, the flavour structure of the dipole operator will be similar to the Yukawa structure, but, in general, not exactly proportional to the Yukawa matrices As a consequence, such a flavour dynamics (e.g. a Froggatt-Nielsen-like model based on some flavour symmetries) will be severely constrained by the requirement that the muon dipole is as large as needed to account for the anomaly, simultaneously evading the stringent bounds on the flavourviolating counterparts of such operator, inducing the lepton flavour violating (LFV) decays → γ (for a recent review on LFV see [15]). It is the elements of this matrix that are constrained as shown in Eqs. (8–10) and (14–16)

Charged lepton Yukawa structure

Flavour structure of the dipole matrix

Flavour symmetries

A4 symmetry

A5 CP symmetry

Conclusions