Short Distance Coefficients and the Vanishing of the Lepton Asymmetry in $B\to V\ell^+\ell^-$

Abstract

We derive a condition the short distance coefficients governing $b\to (s,d)\ell^+\ell^-$ transitions must satisfy in order for the forward-backward asymmetry to vanish in the exclusive modes $B\to (K^*,\rho)\ell^+\ell^-$. This relation, which is satisfied in the standard model, involves the coefficient entering in $b\to s\gamma$ transitions as well as one of the additional Wilson coefficients present in the leptonic modes. We show that the resulting relation is largely free of hadronic uncertainties, thus constituting a reliable test of the standard model in exclusive rare B decays.