Power corrections to bar B→X_uellbar nu (X_sγ) decay spectra in the ``shape-function'' region

Abstract

Using soft-collinear effective theory (SCET), we examine the 1/m b corrections to the factorization formulas for inclusive semi-leptonic B decays in the endpoint region, where the hadronic final state consists of a single jet. At tree level, we find a new contribution from four-quark operators that was previously assumed absent. Beyond tree level many sub-leading shape-functions are needed to correctly describe the decay process.

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.…”

“…The results are given in (33), (47), (56), (72), and (83). For phenomenological purposes, it is most interesting to study the partialB → X s γ decay rate…”

“…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

“…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]…”