Leptonic flavor from a modular A4 symmetry: UV mediators and SMEFT realizations

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:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>A</a:mi><a:mn>4</a:mn></a:msub></a:math> discrete flavor symmetry in constraining the UV dynamics, giving rise to dimension-six SMEFT operators involving leptons. We consider renormalizable interactions between SM fields and heavy mediators, classified according to their <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>A</c:mi><c:mn>4</c:mn></c:msub></c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>A</e:mi><e:mn>4</e:mn></e:msub></e:math> UV mediator irreducible representations 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 renormalization group equation effects in case of vectors.