Strong CP and SUZ$_2$

TL;DR

This paper explores supersymmetric models with Z2 symmetry to address the strong CP problem, analyzing how SUSY breaking impacts the protection of the theta parameter and proposing axion solutions in certain models.

Contribution

It demonstrates that supersymmetry often undermines Z2-based solutions to the strong CP problem, and suggests axion mechanisms as potential remedies in specific SUSY models.

Findings

SUSY breaking generally destroys Z2 protection of θ̄ at tree level.

Without additional structure, Z2-breaking scales are unacceptably tuned.

Axions can relax θ̄ in supersymmetric models like twin Higgs completions.

Abstract

Solutions to the strong CP problem typically introduce new scales associated with the spontaneous breaking of symmetries. Absent any anthropic argument for small $\bar\theta$, these scales require stabilization against ultraviolet corrections. Supersymmetry offers a tempting stabilization mechanism, since it can solve the "big" electroweak hierarchy problem at the same time. One family of solutions to strong CP, including generalized parity models, heavy axion models, and heavy $\eta^\prime$ models, introduces $\mathbb{Z}_2$ copies of (part of) the Standard Model and an associated scale of $\mathbb{Z}_2$-breaking. We review why, without additional structure such as supersymmetry, the $\mathbb{Z}_2$-breaking scale is unacceptably tuned. We then study "SUZ$_2$" models, supersymmetric theories with $\mathbb{Z}_2$ copies of the MSSM. We find that the addition of SUSY typically destroys the $\mathbb{Z}_2$ protection of $\bar\theta=0$, even at tree level, once SUSY and $\mathbb{Z}_2$ are broken. In theories like supersymmetric completions of the twin Higgs, where $\mathbb{Z}_2$ addresses the little hierarchy problem but not strong CP, two axions can be used to relax $\bar\theta$.