Exclusive rare B → K*ℓ⁺ℓ^- decays at low recoil: Controlling the long-distance effects

We present a model-independent description of the exclusive rare decays B̄ → K* e⁺e^- in the low recoil region (large lepton invariant mass q² ∼ m_b²). In this region the long-distance effects from quark loops can be computed with the help of an operator product expansion in I/g, with Q = {m_b, √q²}. Nonperturbative effects up to and including terms suppressed by Λ/Q and m_c²/m_b² 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 U 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 α_s(Q)Λ/m_b, α_s ²(Q), m_c⁴/m_b⁴, and duality violations, and is estimated to be below 10%.