Theory of B → K(*)l+l- decays at high q2: OPE and quark-hadron duality

We develop a systematic framework for exclusive rare B decays of the type B -> K-(*())l(+)l(-) at large dilepton invariant mass q(2). It is based on an operator product expansion (OPE) for the required matrix elements of the nonleptonic weak Hamiltonian in this kinematic regime. Our treatment differs from previous work by a simplified operator basis, the explicit calculation of matrix elements of subleading operators, and by a quantitative estimate of duality violation. The latter point is discussed in detail, including the connection with the existence of an OPE and an illustration within a simple toy model.