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

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 -> e + gamma and mu -> 3e decays and mu -> e conversion in nuclei. In order to examine numerically, two modular flavor A4 models are taken. The SUSY breaking scale is significantly constrained by inputting the observed upper bound of the mu -> e +gamma decay. The SUSY mass scale is larger than around 8 TeV and 5 TeV for the two A4 models, respectively. Therefore, the current experimental upper bound for the mu -> e + gamma decay corresponds to the new physics of the SUSY particle at the 5-10 TeV scale in the modular flavor models. The SUSY scale will be explored by future experiments of lepton flavor violation up to 8 - 17 TeV. The predicted branching ratio depends on a modulus tau significantly. It decreases of one order at the large Im tau. We also calculate the branching ratios of tauon decays to e + gamma and mu + gamma. Predicted ones are at most O(10(-15)), which are much below the current experimental bounds. (C) 2021 The Author(s). Published by Elsevier B.V.