  We examine the implications of the hypothesis that the decays of the b-quark
occur via pure right-handed couplings. We show that the existing lower limits
on neutrinoless double beta decay imply that any gauge model realizing this
idea must have either an $L_e-L_\mu$ or $L_e-L_\tau$ symmetry. We then show
that constraints of cosmology together with observations from SN1987A imply
that the right-handed neutrinos in this model must be heavier than about 100
MeV in general. In one special case with the $L_e-L_\mu$ symmetry, the
$\nu_{\tau_R}$ is heavier than 2 GeV so that this particular version of the
model is already ruled out.
