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Dominant One-Loop Seesaw Contribution Induced by Non-Invertible Fusion Algebra

Monal Kashav

Abstract

The topological classification of the one-loop Weinberg operator at dimension-5 enables a systematic categorization of radiative neutrino mass models. Among these, the category consisting loop-extended seesaw frameworks is theoretically appealing but conventional discrete or continuous symmetries (\emph{e.g.}, $U(1)$ or $\mathbb{Z}_M$) cannot genuinely forbid the corresponding tree-level contributions, making loop dominance difficult to realize. We show that \textit{non-invertible selection rules} (NISRs) naturally enforce the absence of tree-level terms while ensuring a dominant one-loop contribution. Intriguingly, the same non-invertible structure also stabilizes the dark matter candidate, providing a unified radiative origin of neutrino mass and dark sector stability. In particular, we focus on the T4-2-$i$ topology which embodies a type-II one-loop seesaw and demonstrate its natural realization from $Z_{7}$ Tambara--Yamagami (TY) fusion algebra.

Dominant One-Loop Seesaw Contribution Induced by Non-Invertible Fusion Algebra

Abstract

The topological classification of the one-loop Weinberg operator at dimension-5 enables a systematic categorization of radiative neutrino mass models. Among these, the category consisting loop-extended seesaw frameworks is theoretically appealing but conventional discrete or continuous symmetries (\emph{e.g.}, or ) cannot genuinely forbid the corresponding tree-level contributions, making loop dominance difficult to realize. We show that \textit{non-invertible selection rules} (NISRs) naturally enforce the absence of tree-level terms while ensuring a dominant one-loop contribution. Intriguingly, the same non-invertible structure also stabilizes the dark matter candidate, providing a unified radiative origin of neutrino mass and dark sector stability. In particular, we focus on the T4-2- topology which embodies a type-II one-loop seesaw and demonstrate its natural realization from Tambara--Yamagami (TY) fusion algebra.
Paper Structure (9 sections, 29 equations, 1 figure, 2 tables)

This paper contains 9 sections, 29 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. One-Loop Topologies under Conventional and Non-Invertible Symmetries
  3. Fusion Algebras: Invertible vs. Non-Invertible
  4. Discrete Invertible Symmetry Constraints on Loop Dynamics
  5. Non-Invertible Fusion Effects on T4-2-i Realizations
  6. Dark Matter Stability from the Non-Invertible ElementX
  7. Summary AND Discussions
  8. Non-Invertible TY Fusion Algebra
  9. Phase Rephasing of the Neutrino Mass Matrix

Figures (1)

  • Figure 1: Schematic of general T4-2-i topological diagram corresponding to one--loop Type-II seesaw.