  We investigate the possibility whether the tensions with SM expectations
observed in several b -> sll transitions, including hints for lepton flavour
non-universality, could be due to the decay of B into a new light resonance. We
find that qualitative agreement with the data can be obtained with a light
vector resonance dominantly decaying invisibly. This scenario predicts a shift
in the muon anomalous magnetic moment that could explain the long-standing
discrepancy. The most stringent constraint comes from searches for B decays
with missing energy. A striking prediction is a strong q^2 dependence of the
lepton flavour universality ratios R_K and R_K* that should allow to clearly
confirm or rule out this possibility experimentally. We also comment on the
possible connection of the invisible decay product with Dark Matter.

High Energy Physics - Phenomenology