SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model

TL;DR

This paper explores how modular flavor symmetry, specifically $S_3$, constrains SUSY GUT models, and demonstrates that collider and dark matter constraints can significantly restrict the model's parameter space, aligning with observed flavor structures.

Contribution

It introduces a framework for applying collider and dark matter constraints to $S_3$ modular flavor models within SUSY GUTs, showing these constraints can narrow down viable parameter ranges.

Findings

Constraints from collider and DM data restrict modulus parameters.

The UV-completed $S_3$ SU(5) GUT model can reproduce SM flavor structures.

The approach is applicable to other modular flavor symmetry models.

Abstract

Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale. So, in realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can also be used to constrain the possible values of the modulus parameter. In the first part of this work, we discuss the possibility that the $S_3$ modular symmetry can be preserved by the fixed points of $T^2/Z_N$ orbifold, especially from $T^2/Z_2$. To illustrate the additional constraints from collider etc on modular flavor symmetry models, we take the simplest UV SUSY-completion $S_3$ modular invariance SU(5) GUT model as an example with generalized gravity mediation SUSY breaking mechanism. We find that such constraints can indeed be useful to rule out a large portion of the modulus parameters. Our numerical results show that the UV-completed model can account for both the SM (plus neutrino) flavor structure and the collider, DM constraints. Such discussions can also be applied straightforwardly to other modular flavor symmetry models, such as $A_4$ or $S_4$ models.