  A new model of radiative neutrino masses generated via two-loop diagrams is
proposed involving a charge 2/3 vector-like quark and a doublet of leptoquark
scalars. This model predicts one of the neutrinos to be massless and admits
both the normal and inverted neutrino mass hierarchies with correlated
predictions for l_i \rightarrow l_j + \gamma branching ratios. New
contributions to CP violation in B_s-\bar{B}_s mixing arise in the model
through leptoquark box diagrams, which can explain the anomalous dimuon events
reported by the DO collaboration. These leptoquarks, with masses below 500 GeV,
also provide a natural resolution to the apparent discrepancy in the measured
values of the CP violation parameters \sin2\beta and \epsilon_K.
