Phenomenological implications of a class of non-invertible selection rules

TL;DR

The paper addresses how non-invertible fusion algebras yield non-invertible selection rules (NISRs) in four-dimensional particle physics and their phenomenological consequences. It develops a general spurion-based framework and applies it to two minimal SM extensions: a real scalar obeying Fibonacci fusion rules and a dark-matter model based on Ising fusion rules, highlighting tree-level exactness, loop-induced processes, and the groupification mechanism. For the Fibonacci case, single-$s$ processes are loop-induced while multi-$s$ scatterings can occur at tree or loop level, with $\lambda'_{sh}\sim \frac{\lambda_3 \lambda_{sh}}{16\pi^2}$ after groupification; for Ising, an all-loop $\mathbb{Z}_2$ symmetry explains DM stability and constrains couplings via Ising fusion rules. The approach offers a unified language for non-invertible effects in beyond-Standard-Model phenomenology and points to systematic spurion analyses and potential collider, DM, and gravitational-wave signatures, including extensions to multi-scalar sectors.

Abstract

Through well-motivated models in particle physics, we demonstrate the power of a general class of selection rules arising from non-invertible fusion algebras that are only exact at low orders in perturbation theory. Surprisingly, these non-invertible selection rules can even be applied to the minimal extension of the Standard Model, which is to add a gauge-singlet real scalar. In this model, we show that Fibonacci fusion rules lead to experimentally testable features for the scattering processes of the real scalar. We anticipate that this class of non-invertible selection rules can be applied to a wide range of models beyond the Standard Model. To further strengthen our methodology, we discuss a dark matter model based on the Ising fusion rules, where the dark matter is labeled by the non-invertible element in the algebra, hence its stability is preserved at all loop orders.

Figures (5)

• Figure 1: A cartoon showing the scattering processes of the real scalar $s$ and the SM particles whose interactions are constrained by the Fibonacci fusion rules as in Eq. \ref{['eq:fib']}. All the single-$s$ scatterings must be loop induced (denoted by the gray blob), while the multi-$s$ scatterings are present at either tree or loop levels (denoted by the white blob) in perturbation theory. If the real scalar is discovered by future experiments, one can potentially test the Fibonacci fusion rules in these scattering processes.
• Figure 2: A cartoon showing the scattering processes in the DM model with the constraints imposed by the Ising fusion rules. The scattering $s\to H^\dagger H$ must be loop induced (denoted by the gray blob), while $s\to \chi\chi$ and $\chi\chi \to \chi\chi$ can be present at tree level (denoted by the white blob) in perturbation theory. These scattering processes are relevant for DM phenomenology and can potentially be tested in experiments.
• Figure A1: Diagrammatic illustration of Eqs. \ref{['eq:groupification_1']} and \ref{['eq:groupification_2']}, where the two particles labeled by $x$ and $y$ become indistinguishable at the one-loop level due to quantum correction.
• Figure B1: Diagrammatic illustration of groupification for the Fibonacci fusion algebra, which is concretely realized in the real scalar model. Specifically, here we consider the three-point vertex $s|H|^2$.
• Figure C1: Diagrammatic illustration of groupification for the Ising fusion algebra, which is concretely realized in the dark matter model. Specifically, we consider the three-point vertex $s^3$ here.