On the Resummed Hadronic Spectra of Inclusive B Decays

Abstract

In this paper we investigate the hadronic mass spectra of inclusive B decays. Specifically, we study how an upper cut on the invariant mass spectrum, which is necessary to extract V_{ub}, results in the breakdown of the standard perturbative expansion due to the existence of large infrared logs. We first show how the decay rate factorizes at the level of the double differential distribution. Then, we present closed form expressions for the resummed cut rate for the inclusive decays B -> X_s gamma and B -> X_u e nu at next-to-leading order in the infrared logs. Using these results, we determine the range of cuts for which resummation is necessary, as well as the range for which the resummed expansion itself breaks down. We also use our results to extract the leading and next to leading infrared log contribution to the two loop differential rate. We find that for the phenomenologically interesting cut values, there is only a small region where the calculation is under control. Furthermore, the size of this region is sensitive to the parameter \barΛ. We discuss the viability of extracting V_{ub} from the hadronic mass spectrum.

arXiv comment18 pages, 5 figures, minor changes

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Cited by in corpus (15)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Hard Scattering Factorization from Effective Field Theory
• Shape function effects in B -> X_s gamma and B -> X_u l nu decays
• Sudakov resummation of multiparton QCD cross sections
• Inclusive spectra in charmless semileptonic B decays by Dressed Gluon Exponentiation
• Factorization for Power Corrections to B->Xs gamma and B-> Xu e nu
• Soft-Gluon Resummation for Bottom Fragmentation in Top Quark Decay
• Shape-Function Effects and Split Matching in B-> Xs l+ l-
• Determinations of |Vub| from Inclusive Semileptonic B Decays with Reduced Model Dependence
• A consistent resummation of mass and soft logarithms in processes with heavy flavours
• T--odd correlations in (B -> K* l^+ l^-) decay beyond standard model
• Subleading shape function contributions to the hadronic invariant mass spectrum in B -> X_u l νdecay
• Universality and m_X cut effects in B -> Xs l+ l-
• Determination of V_ub from semileptonic B decays