B meson light-cone distribution amplitudes in the heavy-quark limit

We investigate the B meson light-cone distribution amplitudes in the heavyquark limit which are relevant for the QCD factorization approach for the exclusive B meson decays. We derive exact relations between twoand three-particle distribution amplitudes from the QCD equations of motion and heavy-quark symmetry constraint. As solution of these relations, we give representations for the quark-antiquark distribution amplitudes in terms of independent dynamical degrees of freedom. In particular, we find that the Wandzura-Wilczek-type contributions are determined uniquely in analytic form in terms of Λ̄, a fundamental mass parameter of heavy-quark effective theory, and that both leadingand higher-twist distribution amplitudes receive the contributions of multi-particle states with additional gluons. DESY 01-135 HUPD-0108 JUPD-0191 September 2001 hep-ph/0109181 ∗JSPS Research Fellow. Recently systematic methods based on the QCD factorization have been developed for the exclusive B meson decays into light mesons [1, 2, 3, 4, 5] (for other approaches see, e.g. [6]). Essential ingredients in this approach are the light-cone distribution amplitudes for the participating mesons, which constitute nonperturbative long-distance contribution to the factorized amplitudes [7]. As for the light mesons (π, K, η, ρ, ω, K, φ) appearing in the final state, systematic model-independent study of the lightcone distributions exists for both leading and higher twists [8, 9, 10, 11]. On the other hand, unfortunately, the light-cone distribution amplitudes for the B meson are not well-known at present and provide a major source of uncertainty in the calculations of the decay rates. In this Letter, we demonstrate that heavy-quark symmetry and constraints from the equations of motion determine a unique analytic solution for the B meson light-cone distribution amplitudes within the two-particle Fock states. We also derive the exact integral representations for the effects of higher Fock states with additional gluons. A complete set of the B meson distribution amplitudes are constructed in terms of independent dynamical degrees of freedom, which satisfies all relevant QCD constraints. In the heavy-quark limit, the B meson matrix elements obey the heavy-quark symmetry, and is conveniently described by the heavy-quark effective theory (HQET) [12, 13]. Following Refs. [14, 2, 3], we introduce the quark-antiquark light-cone distribution amplitudes φ̃±(t) of the B meson in terms of vacuum-to-meson matrix element of nonlocal light-cone operators in the HQET: 〈0|q̄(z)Γhv(0)|B̄(p)〉 = − ifBM 2 Tr [