Leptonic Flavor from Modular $A_4$: UV Mediators and SMEFT Realizations

TL;DR

This paper explores how the $A_4$ flavor symmetry constrains UV completions of SMEFT operators involving leptons, analyzing mediator classifications and their phenomenological implications for flavor observables.

Contribution

It introduces a modular $A_4$ framework for classifying UV mediators and systematically studies their effects on lepton flavor processes within SMEFT.

Findings

Classified $A_4$ UV mediators based on modular symmetry properties.

Analyzed both tree-level and loop-level contributions to lepton flavor observables.

Provided phenomenological constraints on mediator models from current experimental data.

Abstract

The absence of direct evidence for new physics at current collider energies motivates the study of indirect effects within the framework of the Standard Model Effective Field Theory (SMEFT). In this work, we investigate the role of the $A_4$ discrete flavor symmetry in constraining the UV dynamics, giving rise to dimension-6 SMEFT operators involving leptons. We consider renormalizable interactions between SM fields and heavy mediators, classified according to their $A_4$ transformation properties in the modular framework, where Yukawa structures are encoded in modular forms. Restricting our analysis to UV interactions with at most a single modular form insertion, we study the resulting classification of $A_4$ UV mediator irreps and explore their implications across a range of observables, including both lepton-flavor-conserving and lepton-flavor-violating processes. A detailed phenomenological analysis is carried out, incorporating both tree-level and one-loop matching contributions for scalar and fermionic mediators, as well as leading-log RGE effects in case of vectors.