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) x U(1)pQ -> SU(3)(e) and produces a QCD axion. Small values of the CP-violating 0 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 (theta) over bar < 10(-10), even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level.