A Roadmap for neutrino charge assignments in $U(2)_F$ Flavor Models: Implications for LFV processes and leptonic anomalous magnetic moments

TL;DR

This paper explores alternative neutrino charge assignments in a $U(2)_F$ flavor model, analyzing implications for lepton flavor violation and the muon anomalous magnetic moment within the SMEFT framework, without adding new symmetries.

Contribution

It introduces new neutrino charge assignments in a $U(2)_F$ model that generate Majorana neutrino masses via the see-saw mechanism without extra symmetries or isomorphisms.

Findings

Current LFV decay limits conflict with the $(g-2)_$ measurement in these models.

The models suggest $(g-2)_$ must align closely with the Standard Model.

Flavor symmetry may not fully explain the muon anomalous magnetic moment.

Abstract

We build upon a simple $U(2)_F$ model of flavor, in which all fermion masses and mixing hierarchies arise from powers of two small parameters controlling $U(2)_F$ breaking. In the original formulation, an isomorphism to the discrete $D_6\times U(1)_F$ symmetry was invoked to generate a Majorana neutrino mass term. Here, we retain the successful features of that model for the charged leptons and quarks, while exploring alternative neutrino charge assignments within the $U(2)_F$ framework. This approach allows us to generate Majorana neutrino masses via the see-saw mechanism without introducing any additional symmetries nor invoking any isomorphism. We further examine the implications of our models for Lepton Flavor Violating (LFV) decays, analyzing the processes $\mu\rightarrow e\gamma$, $\tau\rightarrow\mu\gamma$ and $\tau\rightarrow e\gamma$ and their connection with the leptonic anomalous magnetic moments. We show that within the Standard Model Effective Field Theory (SMEFT) approach the current limits on the branching ratios of $\mu\rightarrow e\gamma$ LFV decays obtained in our $U(2)_F$ models are not compatible with the central value of the recent measurement of the $(g-2)_\mu$, thereby suggesting that either $(g-2)_\mu$ must be very close to the Standard Model predictions, as the latest experimental and theoretical results seem to suggest, or the invoked flavor symmetry is not appropriate to describe an anomalous muon magnetic moment.