QFT
In the literature: open
Observable consequences of non-invertible symmetries in the Standard Model
In plain words
Some symmetries of the Standard Model, thought to be destroyed by quantum effects, survive in a form with no undo. Which measurable predictions follow from them is unclear.
Precise statement
The ABJ-anomalous axial U(1) symmetries of QED and of the Standard Model retain non-invertible rational-angle subgroups (Choi, Lam, Shao 2022; Cordova, Ohmori 2022). Determine the exact selection rules and constraints on observables (neutral pion decay, axion couplings, neutrino masses) that follow from them beyond ordinary anomaly matching.
What would settle it
A derivation of an exact constraint on a measurable quantity that follows from the non-invertible symmetry and not from ordinary anomaly matching.