The Minimal Supersymmetric Standard Model with Non-Invertible Selection Rules

TL;DR

The paper introduces a Minimal Supersymmetric Standard Model where non-invertible selection rules, realized by gauging the outer automorphism of a discrete symmetry, dictate fermion Yukawas and force diagonal soft masses. This alignment suppresses FCNCs while producing realistic quark and lepton mass textures and remains stable under MSSM RG evolution. Numerical scans with random ${\cal O}(1)$ coefficients show suppressed flavor violation in leptons and quarks, with down-type quarks offering the strongest constraints, yet overall compatibility with current data for TeV-scale superpartners. The framework also allows possible tensions or enhancements in certain Kaon and Bs decays, and is discussed in the context of potential UV completions, including orbifold GUTs and combined horizontal symmetry scenarios. The approach offers a cohesive mechanism to address both the origin of flavor and SUSY flavor problems, with testable implications for future flavor observables.

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 $μ\to e γ$ 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.

Figures (4)

• Figure 1: Distributions for $\Delta M_K^{\rm SUSY}$ and $\varepsilon_K^{\rm SUSY}$ in our model. The sold blue line corresponds to the mean value, and the 95% CI is between two dashed blue lines.
• Figure 2: Distributions for $\Delta M_{B_d}^{\rm SUSY}$ and $\Delta M_{B_s}^{\rm SUSY}$ in our model. The sold blue line corresponds to the mean value, and the 95% CI is between two dashed blue lines.
• Figure 3: Distribution for $|d_n|$ in our model. The sold blue line corresponds to the mean value, and the 95% CI is between two dashed blue lines.
• Figure 4: Distribution for ${\rm BR} (B \to X_s \gamma)$ in our model. The sold blue line corresponds to the mean value, and the 95% CI is between two dashed blue lines.