Enhanced Three-Particle Contribution to Electroweak Penguin $B$-Meson Decays

Abstract

We compute for the first time the subleading twist correction to the exclusive rare $b \to \left \{s, d \right \} \ell^{+} \ell^{-}$ decays from the three-particle $B$-meson distribution amplitude at next-to-leading order accuracy by employing the soft-collinear effective theory. This constitutes the last missing ingredient for the complete factorization analysis of the hadronic matrix element of the weak effective Hamiltonian at leading power in the heavy quark expansion. Incorporating further a variety of the next-to-next-to-leading-order QCD corrections to the spectator-scattering amplitude and the weak annihilation topology, we then present the improved field-theoretic predictions for phenomenologically interesting observables in the electroweak penguin $B \to \left \{K, \pi \right \} \ell^{+} \ell^{-}$ decays.