QCD axion from a spontaneously broken B - L gauge symmetry

In this paper, we show that the Peccei-Quinn (PQ) symmetry with a good quality can be realized in a simple B -L extension of the minimal supersymmetric standard model. The PQ symmetry is a remnant of the B - L gauge symmetry at the renormalizable level. Besides, the sufficient quality of the PQ symmetry is preserved by a non anomalous discrete gauged R-symmetry and a small gravitino mass m ₃ ≪ 100 GeV. A viable mass range is $$ eV which allows a high reheating temperature and many baryogenesis scenarios typified by the thermal leptogenesis without any astrophysical and cosmological problems. Such a light gravitino may be tested in the future 21cm line observations.