A composite axion from a supersymmetric product group

A global U(1)PQ symmetry is protected from gravitational effects in the s-confining SU(N)k product group theory with A+4Q+NQ¯ 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) × U(1)PQ → SU(3)c and produces a QCD axion. Small values of the CP -violating θ 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 θ¯ < 1 0 − 10, even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level