Inclusive semileptonicBdecays and the determination of |V_ub|

Abstract

We present "state-of-the-art" theoretical expressions for the triple differential ¯ B → X u l − ¯ ν decay rate and for the ¯ B → X s γ photon spectrum, which incorporate all known contributions and smoothly interpolate between the "shape-function region" of large hadronic energy and small invariant mass, and the "OPE region" in which all hadronic kinematical variables scale with M B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m b enters indirectly through the properties of the leading shape function, which can be determined by fitting the ¯ B → X s γ photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for ¯ B → X u l − ¯ ν decay distributions, allowing for a precise determination of |V ub |. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(α 2 s) terms. Predictions are presented for partial ¯ B → X u l − ¯ ν decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.

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

“…The same shape function parameterizes the leading bound-state effects in the inclusive semileptonic decayB → X u lν. As a result, a precise measurement of the photon spectrum can be used to derive useful hadronic input for the analysis ofB → X u lν decay spectra, and in this way enable a precise determination of |V ub | [13,14]. One goal of the present paper is to complete the analysis of non-perturbative effects on theB → X s γ photon spectrum at subleading order in the heavy-quark expansion.…”

“…The partially inclusive rates obtained experimentally are defined as integrals over the endpoint region E 0 < E γ < M B /2. The shape of the photon spectrum in the region above 2 GeV is most useful for extracting information that can be used to determine |V ub | fromB → X u lν decay distributions [13,14]. Note that in the relevant region of phase space the variable ∆ = m b − 2E 0 is a hadronic scale of order Λ QCD , which is much smaller than the hard scale m b of the process.…”

Inclusive semileptonicBdecays and the determination of |Vub|

“…In the analysis of [8] a set of about 80 different functional forms, inspired by those already present in the literature (exponential, Gaussian, Roman, hyperbolic), is tested and the related uncertainty on |V ub | turns out to be rather small (see Sec. 3).…”

“…In [8] a similar procedure was undertaken for the case of semileptonic decays, where many complications arise, mostly due to the kinematics taking place at different q 2 . In the following we illustrate the main features of this procedure and show some meaningful results.…”

“…The pole mass is better traded with a running mass m b (µ). To this purpose, perturbative corrections to order O(α 2 s β 0 ) are calculated anew in [8] in the presence of a "hard" Wilsonian cutoff µ ∼ 1 GeV. This new scale separates the perturbative regime of gluons with energies larger than µ from the "soft" (nonperturbative) regime of gluons with energies lower than µ.…”