Spectator interactions and factorization in B -> pi ell nu decay

Abstract

We investigate the factorization of different momentum modes that appear in matrix elements for exclusive B meson decays into light energetic particles for the specific case of B -> pi form factors at large pion recoil. We first integrate out hard modes with virtualities of order m_b^2 (m_b being the heavy quark mass), and then hard-collinear modes with virtualities m_b Lambda (Lambda being the strong interaction scale). The resulting effective theory contains soft and collinear fields with virtualities Lambda^2. We prove a previously conjectured factorization formula for B -> pi form factors in the heavy quark limit to all orders in alpha_s, paying particular attention to `endpoint singularities' that might have appeared in hard spectator interactions.