The Minimal Supersymmetric Standard Model with Non-Invertible Selection Rules

TL;DR

This paper proposes a novel MSSM framework using non-invertible selection rules to naturally generate realistic flavor textures and suppress flavor-changing neutral currents, aligning with experimental constraints.

Contribution

It introduces a new mechanism based on non-invertible selection rules from gauged automorphisms to address flavor and FCNC issues in supersymmetry.

Findings

Yukawa textures reproduce observed fermion masses and mixings.

Flavor-violating effects are within experimental limits.

Yukawa and soft terms are stable under RG evolution.

Abstract

We investigate a framework of the Minimal Supersymmetric Standard Model (MSSM) in which the quark and lepton flavor structure and suppression of flavor-changing neutral currents (FCNCs) are governed by non-invertible selection rules. By implementing such non-group-like fusion rules for matter fields, arising from gauging the outer automorphism $\mathbb{Z}_2$ of a discrete $\mathbb{Z}_N$ symmetry, we obtain realistic Yukawa textures that reproduce the observed quark and lepton masses and mixings while ensuring diagonal soft supersymmetry (SUSY) breaking masses and hence suppressing dangerous FCNC processes. We analyze mass insertion parameters under random $\mathcal{O}(1)$ coefficients and find that all flavor-violating effects are consistent with experimental limits on processes such as $\mu \to e \gamma$ and meson mixings. We show that the Yukawa textures and soft terms remain stable under renormalization group evolution. Our results demonstrate that non-invertible selection rules provide a compelling new mechanism to address both the flavor structure and FCNC problems in supersymmetric models.