Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models

TL;DR

This paper investigates how the modulus F-term influences soft SUSY breaking in modular flavor models of leptons, deriving specific patterns and analyzing phenomenological implications like lepton flavor violation, with numerical constraints on SUSY scales from experimental bounds.

Contribution

It introduces the impact of modulus F-term on soft SUSY breaking in modular flavor models and provides numerical constraints on SUSY scales based on lepton flavor violation data.

Findings

SUSY mass scale constrained to >8 TeV and >5 TeV in two A4 models.

Branching ratio for μ → e + γ decay is sensitive to the modulus τ.

Predicted tau decay branching ratios are well below current experimental bounds.

Abstract

We study the soft supersymmetry (SUSY) breaking terms due to the modulus F-term in the modular flavor models of leptons. It is found that the soft SUSY breaking terms are constrained by the modular forms, and specific patterns are derived. Those phenomenological implications are discussed in such as the lepton flavor violation, $\mu \rightarrow e + \gamma$ decay. In order to examine numerically, two modular flavor $A_4$ models are taken. The SUSY breaking scale is significantly constrained by inputting the observed upper bound of the $\mu \rightarrow e + \gamma$ decay. The SUSY mass scale is larger than around $8$ TeV and $5$ TeV for the two $A_4$ models, respectively. Therefore, the current experimental upper bound for the $\mu \to e + \gamma$ decay corresponds to the new physics of the SUSY particle at the $5$ -- $10$ TeV scale in the modular flavor models. The predicted branching ratio depends on a modulus $\tau$ significantly. It decreases of one order at the large ${\rm Im}\,\tau$. We also calculate the branching ratios of tauon decays to $e + \gamma$ and $\mu + \gamma$. Predicted ones are at most ${\cal O}(10^{-15})$, which are much below the current experimental bounds.