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

Abstract

Using methods of effective field theory, factorized expressions for arbitraryB → 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 chargedlepton 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 ub | is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.

A two-loop relation between inclusive radiative and semileptonicB-decay spectra

“…Here m b is defined in the shape-function scheme at a scale µ * = 1.5 GeV, m s is the running mass in the MS scheme evaluated at 1. =μ def = 1.5 GeV, which are motivated by the underlying dynamics of inclusive processes in the shape-function region [7,15].…”

“…A sensitivity to the hard scale µ h enters into f (k) via the appearance of H u (y, µ h ) in (15). Because of the polynomial nature of j(L, µ i ), all we ever need are moments of the hard function with respect to ln y.…”

“…Separation of the two scales µ h and µ i allows for the logarithms in matching corrections to be small, while logarithms of the form ln µ h /µ i , which appear at every order in perturbation theory, are resummed in a systematic fashion and give rise to the RG evolution functions U(µ h , µ i ) and a Γ (µ h , µ i ) [15]. The leading-power jet function J(p 2 , µ i ) entering the expressions for F i is universal and has been computed at one-loop order in [14,15]. More recently, the two-loop expression for J has been obtained apart from a single unknown constant [16], which is the two-loop coefficient of the local δ(p 2 ) term.…”

Precision direct photon andW-boson spectra at highpTand comparison to LHC data

“…Because of the relationŝ+t+û = m 2 X +M 2 V the δ-function parts effectively only depend on a single variable. The ⋆-distributions are generalizations of the usual +-distributions to dimensionful variables [36]. A N n LO computation would give distributions with logarithms up to ln 2n−1 (m X /µ) in the numerator.…”

Factorization at subleading power and irreducible uncertainties in $ \bar{B} \to {X_s}\gamma $ decay

“…Using methods of effective field theory, we propose a novel factorization formula valid at any order in the 1/m b expansion, which is a generalization of the familiar soft-collinear factorization formula [27][28][29][31][32][33] dΓ(B → X u lν) = …”