Key points are not available for this paper at this time.
A bstract 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 A + 4 Q + N 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) × 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.
Lillard et al. (Wed,) studied this question.