Exclusive rareB→K*ℓ+ℓ−decays at low recoil: Controlling the long-distance effects

We present a model-independent description of the exclusive rare decays $\overline{B}\to K^{*}{e}^{+}{e}^{-}$ in the low recoil region (large lepton invariant mass $q^2\sim m_b^2$). In this region the long-distance effects from quark loops can be computed with the help of an operator product expansion in $1/Q$, with $Q=\{m_b,\sqrt{q^2}\}$. Nonperturbative effects up to and including terms suppressed by $\Lambda /Q$ and $m_c^2/m_b^2$ relative to the short-distance amplitude can be included in a model-independent way. Based on these results, we propose an improved method for determining the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ from a combination of rare and semileptonic $B$ and $D$ decays near the zero recoil point. The residual theoretical uncertainty from long-distance effects in this $|V_{ub}|$ determination comes from terms in the operator product expansion of order ${\alpha }_s(Q)\Lambda /m_b$, ${\alpha }_s^2(Q)$, $m_c^4/m_b^4$, and duality violations, and is estimated to be below 10%.