Factorization and shape-function effects in inclusive B-meson decays

Abstract

Using methods of effective field theory, factorized expressions for arbitrary B ¯ → X u l − ν ¯ decay distributions in the shape-function region of large hadronic energy and moderate hadronic invariant mass are derived. Large logarithms are resummed at next-to-leading order in renormalization-group improved perturbation theory. The operator product expansion is employed to relate moments of the renormalized shape function with HQET parameters such as m b , Λ ¯ and λ 1 defined in a new physical subtraction scheme. An analytic expression for the asymptotic behavior of the shape function is obtained, which reveals that it is not positive definite. Explicit expressions are presented for the charged-lepton energy spectrum, the hadronic invariant mass distribution, and the spectrum in the hadronic light-cone momentum P + = E H − | P → H | . A new method for a precision measurement of | V u b | is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.