A high quality composite axion

The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)_PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)_PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N)_L × SU(N) × SU(N)_R × U(1)_X product gauge group, achieving $\left(\overline{\theta }\right)$ < 10⁻¹¹ for an SU(5) model with f_a ≲ 3 × 10¹¹ GeV. This construction leads to low energy predictions such as a U(1)_X gauge symmetry, and for X = B − L engineers a naturally $O$(TeV) value for the μ parameter of the MSSM.