A Composite Axion from a Supersymmetric Product Group

TL;DR

This paper proposes a composite axion model within a supersymmetric product group framework, demonstrating how it can naturally suppress the QCD $CP$-violation parameter without fine-tuning, using s-confining $SU(N)^k$ theories.

Contribution

It introduces a novel supersymmetric product group model that protects the $U(1)_{PQ}$ symmetry from gravitational effects and generates a QCD axion with naturally small $CP$ violation.

Findings

A global $U(1)_{PQ}$ symmetry is protected from gravitational effects.

The model produces a QCD axion through spontaneous symmetry breaking.

Small $ar heta$ values are achievable with product groups as small as $N=7$.

Abstract

A global $U(1)_\text{PQ}$ symmetry is protected from gravitational effects in the s-confining $SU(N)^k$ product group theory with $A+4Q +N\overline{Q}$ matter. If the $SU(4)$ family symmetry is gauged and an appropriate tree-level superpotential is added, then the dynamically generated superpotential spontaneously breaks $SU(4)\times U(1)_\text{PQ} \rightarrow SU(3)_c$ and produces a QCD axion. Small values of the $CP$-violating $\theta$ parameter are then possible without any fine-tuning, as long as the product group is suitably large. By introducing a second copy of the s-confining $SU(N)$ product group also coupled to the gauged $SU(4)$, we find that values as small as $N=7$ are consistent with $\bar\theta<10^{-10}$, even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level.