  The relevant phenomenology and the best search schemes of a
subelectroweak-scale gauge boson can be vastly different depending on its
coupling. For instance, the rare decay into a light gauge boson and the high
precision parity test can be sensitive if it has an axial coupling. The minimal
gauge extension of the standard model with the U(1)_{B-L + xY} requires only
three right-handed neutrinos, well-suited to the current neutrino mass and
mixing data, and no additional exotic matter fields. We study the light gauge
boson of this symmetry in detail including its axial coupling property from the
hypercharge shift.
