Spectator interactions and factorization in B→π l ν decay

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→π 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_bΛ (Λ being the strong interaction scale). The resulting effective theory contains soft and collinear fields with virtualities Λ². We prove a previously conjectured factorization formula for B → π form factors in the heavy quark limit to all orders in α_s, paying particular attention to ‘endpoint singularities’ that might have appeared in hard spectator interactions. PACS: 12.39.St Factorization — 13.20.He