Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion

TL;DR

This paper explores how non-invertible Peccei-Quinn symmetry in a two-Higgs-doublet model can naturally explain alignment without decoupling and revive the visible axion, using a novel UV theory involving quark monopoles.

Contribution

It introduces a new use of non-invertible symmetry in model building to naturally explain small parameters and alignment in the 2HDM without requiring new fermions.

Findings

Realizes natural alignment without decoupling in 2HDM

Revives the Weinberg-Wilczek axion in a UV-complete model

Uses color-flavor monopoles in an $SU(9)$ theory for UV completion

Abstract

We identify $m_{12}^2$ as a spurion of non-invertible Peccei-Quinn symmetry in the type II 2HDM with gauged quark flavor. Thus a UV theory which introduces quark color-flavor monopoles can naturally realize alignment without decoupling and can furthermore revive the Weinberg-Wilczek axion. As an example we consider the $SU(9)$ theory of color-flavor unification, which needs no new fermions. This is the first model-building use of non-invertible symmetry to find a Dirac natural explanation for a small $\textit{relevant}$ parameter.