Subleading Shape Functions in Inclusive B Decays

Abstract

The contributions of subleading shape functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft-collinear and heavy-quark effective theory. At tree-level, the results can be expressed in terms of forward matrix elements of bi-local light-cone operators. Fourquark operators, which arise at O(α s ), are included. Our results are in disagreement with some previous studies of subleading shape-function effects. A numerical analysis ofB → X u l −ν decay distributions suggests that power corrections are small, with the possible exception of the endpoint region of the charged-lepton energy spectrum.

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

“…So far they have been studied only for the direct photon contribution from two insertions of the electromagnetic dipole operator Q 7γ [30][31][32][33]. In the notation of [32], one obtains at tree level…”

“…Note that by definition the external momenta P X , q, and M B v have vanishing perpendicular components. SCET and HQET are the appropriate effective field theories to study the factorization properties of inclusive B-meson decay spectra in the endpoint region [28,29,[31][32][33]. We will need several types of SCET modes for our analysis, each one corresponding to a particular physical scale relevant to the process.…”

“…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) = …”

A complete basis of helicity operators for subleading factorization

“…For example 21) indicates that the P + ⊥ or P − ⊥ operator acts only on the middle field. In general, we can decompose the action of the P ± ⊥ operators into a superposition of terms where P ± ⊥ will act only on a single field within a quark current.…”

“…The description of observables with more complicated dynamics typically relies on factorization theorems and much less is known about the structure of power corrections in these cases. Power corrections have been considered for Drell-Yan [11][12][13][14][15] at O(Λ 2 QCD /Q 2 ), for inclusive B decays in the endpoint region at O((1−z) 0 , (Λ QCD /m b ) 1,2 ) [16][17][18][19][20][21][22][23][24], for exclusive B decays at O(Λ QCD /m b ) [25][26][27][28][29][30][31][32][33], for event shapes τ in e + e − , ep, and pp collisions at O(Λ k QCD /(Qτ ) k ) [13,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], and at O((1 − z) 0 ) for threshold resummation [49][50][51][52][53][54][55][56]…”