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The Minimal Supersymmetric Standard Model with Non-Invertible Selection Rules
High Energy Physics - Phenomenology · Submitted 25 Dec 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.98 | 0.84 | 0.08 | asserted 0.97 |
| s1 | 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. | method 0.74 | 0.93 | 0.18 | asserted 1.00 |
| s2 | 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. | result 0.95 | 0.96 | 0.08 | asserted 0.87 |
| s3 | We show that the Yukawa textures and soft terms remain stable under renormalization group evolution. | result 1.00 | 0.94 | 0.06 | asserted 1.00 |
| s4 | 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. | interpretation 1.00 | 0.92 | 0.96 | asserted 1.00 |
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The paper
Original 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.
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References
How the literature uses it
8 arXiv papers cite this in 8 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 6 papers
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Recently, however, a novel class of symmetries based on non-invertible fusion rules has been developed and begun to find applications in phenomenology [ref] .
Dirac one-loop seesaw in a non-invertible fusion rule · Introduction · 0.88
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In this work, we propose a novel mechanism to realize small VEVs for the exotic scalar quadruplet $H_4$ and quintuplet $H_5$ by employing the Fibonacci fusion rule (FFR), which is recognized as the minimal non‑invertible symmetry and has recently been explored in phenomenological contexts [ref] .
A theoretical account of tiny multi-Higgs vacuum expectation values from non-invertible symmetry · Introduction · 0.80
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Their applications span a wide range of contexts, including quark–lepton texture analyses [ref] , dynamical breaking corrections [ref] , strong CP physics [ref] , dark matter models [ref] , suppression of flavor changing neutral currents [ref] , realization of family-independent matter symmetries [ref] , and generalized CP constructions [ref] .
Dynamical CP Violation from Non-Invertible Selection Rules · Introduction · 0.83
What it cites · 86 sentences without a confident label
Uses the method or tool of 4 papers
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In the present paper, we utilize a non-invertible selection rule realized by $ℤ_2$ gauging of a $ℤ_N$ symmetry [ref] to find viable Yukawa textures in the MSSM framework.
Non-invertible flavor symmetries in magnetized extra dimensions · Introduction · 0.94
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In the present paper, we utilize a non-invertible selection rule realized by $ℤ_2$ gauging of a $ℤ_N$ symmetry [ref] to find viable Yukawa textures in the MSSM framework.
Yukawa textures from non-invertible symmetries · Introduction · 0.94
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The dominant SUSY contribution to $BR (b →s γ)$, mediated by the gluino, is given by [ref] [equation] where we have used the fact that $|(δ^d_RL)_23| = |(δ^d_LR)_32|$.
A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model · $b →s γ$ · 0.84
Uses data or values from 7 papers
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Using the estimated values for slepton masses, $μ$-term and bino mass as well as the current experimental bound of $BR (μ→e γ) < 3.1 ×10^-13$ [ref] , the off-diagonal elements of slepton MI parameters are constrained as $|δ^e| ≲10^-2$, according to the studies in Refs. [ref] .
Constraints on SUSY Lepton Flavour Violation by rare processes · Lepton observables · 0.88
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Using the estimated values for slepton masses, $μ$-term and bino mass as well as the current experimental bound of $BR (μ→e γ) < 3.1 ×10^-13$ [ref] , the off-diagonal elements of slepton MI parameters are constrained as $|δ^e| ≲10^-2$, according to the studies in Refs. [ref] .
Supersymmetric Alignment Models for $(g-2)_{\mu}$ · Lepton observables · 0.88
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Using the estimated values for slepton masses, $μ$-term and bino mass as well as the current experimental bound of $BR (μ→e γ) < 3.1 ×10^-13$ [ref] , the off-diagonal elements of slepton MI parameters are constrained as $|δ^e| ≲10^-2$, according to the studies in Refs. [ref] .
A search for $\mu^+\to e^+\gamma$ with the first dataset of the MEG II experiment · Lepton observables · 0.88
Compares with 1 paper
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We use the above values as input parameters at the unification scale and find the following Yukawa textures at the soft mass scale $M_SUSY = 3 TeV$: [equation] Here, we have shown the SM Yukawa matrices by using $Y_u = Y_u^MSSM sinβ$ and $Y_d, e = Y_d, e^MSSM cosβ$, and the resulting eigenvalues of each Yukawa matrix and CKM parameters are consistent with those in Ref. [ref] .
2510.01312 · Yukawa textures and RG effects · 0.96
Cites as background 25 papers
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For other phenomenological applications, see, e.g., Refs. [ref] .] Such selection rules appear in theories with non-invertible symmetries in various dimensions (see, e.g., Refs. [ref] for reviews).[There have been remarkable developments in applying non-invertible symmetries to particle phenomenology, e.g., the emergence of non-invertible symmetries from Abelian chiral symmetries [ref] and a realization of small Dirac neutrino Yukawa couplings protected by a non-invertible symmetry [ref] .] Moreover, it has turned out that the non-invertible selection rules are motivated by string compactifications, as discussed in type IIB magnetized D-brane models [ref] , heterotic string theory on Calabi-Yau threefolds [ref] , and Abelian and non-Abelian orbifolds [ref] .
Three-loop induced neutrino mass model in a non-invertible symmetry · Introduction · 0.96
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For other phenomenological applications, see, e.g., Refs. [ref] .] Such selection rules appear in theories with non-invertible symmetries in various dimensions (see, e.g., Refs. [ref] for reviews).[There have been remarkable developments in applying non-invertible symmetries to particle phenomenology, e.g., the emergence of non-invertible symmetries from Abelian chiral symmetries [ref] and a realization of small Dirac neutrino Yukawa couplings protected by a non-invertible symmetry [ref] .] Moreover, it has turned out that the non-invertible selection rules are motivated by string compactifications, as discussed in type IIB magnetized D-brane models [ref] , heterotic string theory on Calabi-Yau threefolds [ref] , and Abelian and non-Abelian orbifolds [ref] .
Radiative lepton model in a non-invertible fusion rule · Introduction · 0.96
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For other phenomenological applications, see, e.g., Refs. [ref] .] Such selection rules appear in theories with non-invertible symmetries in various dimensions (see, e.g., Refs. [ref] for reviews).[There have been remarkable developments in applying non-invertible symmetries to particle phenomenology, e.g., the emergence of non-invertible symmetries from Abelian chiral symmetries [ref] and a realization of small Dirac neutrino Yukawa couplings protected by a non-invertible symmetry [ref] .] Moreover, it has turned out that the non-invertible selection rules are motivated by string compactifications, as discussed in type IIB magnetized D-brane models [ref] , heterotic string theory on Calabi-Yau threefolds [ref] , and Abelian and non-Abelian orbifolds [ref] .
A radiative lepton model in a non-invertible fusion rule · Introduction · 0.96
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