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Title: Comparative analysis of nonperturbative effects in B{yields}X{sub u}l{nu}{sub l} decays

Abstract

In order to extract the Cabibbo-Kobayashi-Maskawa matrix element |V{sub ub}| from B{yields}X{sub u}l{nu}{sub l} decays, the overwhelming background from B{yields}X{sub c}l{nu}{sub l} decays must be reduced by appropriate acceptance cuts. We study the nonperturbative effects due to the motion of the b quark inside the B meson on the phenomenologically relevant decay distributions of B{yields}X{sub u}l{nu}{sub l} in the presence of such cuts in a comparative analysis based on shape functions and the parton model in the light cone limit. Comparisons with recent data from the CLEO, BABAR, and BELLE collaborations favor the shape-function approach.

Authors:
; ;  [1];  [2]
  1. II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
  2. (China)
Publication Date:
OSTI Identifier:
21020283
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.074023; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; B MESONS; B QUARKS; CESR STORAGE RING; COMPARATIVE EVALUATIONS; CP INVARIANCE; DISTRIBUTION; GLUON MODEL; GLUONS; KOBAYASHI-MASKAWA MATRIX; LIGHT CONE; MULTIPARTICLE SPECTROMETERS; NEUTRINOS; PARTICLE IDENTIFICATION; QUARK MODEL; SEMILEPTONIC DECAY

Citation Formats

Kniehl, Bernd A., Kramer, Gustav, Yang Jifeng, and Department of Physics, East China Normal University, 3663th Zhong Shan Bei Road, Shanghai 200062. Comparative analysis of nonperturbative effects in B{yields}X{sub u}l{nu}{sub l} decays. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.074023.
Kniehl, Bernd A., Kramer, Gustav, Yang Jifeng, & Department of Physics, East China Normal University, 3663th Zhong Shan Bei Road, Shanghai 200062. Comparative analysis of nonperturbative effects in B{yields}X{sub u}l{nu}{sub l} decays. United States. doi:10.1103/PHYSREVD.75.074023.
Kniehl, Bernd A., Kramer, Gustav, Yang Jifeng, and Department of Physics, East China Normal University, 3663th Zhong Shan Bei Road, Shanghai 200062. Sun . "Comparative analysis of nonperturbative effects in B{yields}X{sub u}l{nu}{sub l} decays". United States. doi:10.1103/PHYSREVD.75.074023.
@article{osti_21020283,
title = {Comparative analysis of nonperturbative effects in B{yields}X{sub u}l{nu}{sub l} decays},
author = {Kniehl, Bernd A. and Kramer, Gustav and Yang Jifeng and Department of Physics, East China Normal University, 3663th Zhong Shan Bei Road, Shanghai 200062},
abstractNote = {In order to extract the Cabibbo-Kobayashi-Maskawa matrix element |V{sub ub}| from B{yields}X{sub u}l{nu}{sub l} decays, the overwhelming background from B{yields}X{sub c}l{nu}{sub l} decays must be reduced by appropriate acceptance cuts. We study the nonperturbative effects due to the motion of the b quark inside the B meson on the phenomenologically relevant decay distributions of B{yields}X{sub u}l{nu}{sub l} in the presence of such cuts in a comparative analysis based on shape functions and the parton model in the light cone limit. Comparisons with recent data from the CLEO, BABAR, and BELLE collaborations favor the shape-function approach.},
doi = {10.1103/PHYSREVD.75.074023},
journal = {Physical Review. D, Particles Fields},
number = 7,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • We investigate the exclusive rare B{sub c{yields}}D{sub (s){nu}l{nu}l} and B{yields}D{sub (s)}l{sup +}l{sup -} (l=e, {mu}, {tau}) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors f{sub {+-}}(q{sup 2}) and f{sub T}(q{sup 2}) are obtained from the analytic continuation method in the q{sup +}=0 frame. While the form factors f{sub +}(q{sup 2}) and f{sub T}(q{sup 2}) are free from the zero mode, the form factor f{sub -}(q{sup 2}) is not free from the zero mode in the q{sup +}=0 frame. We discuss the covariance (i.e. frame independence)more » of our model calculation and quantify the zero-mode contributions to f{sub -}(q{sup 2}) for B{sub c{yields}}D{sub (s)} decays. The branching ratios and the longitudinal lepton polarization asymmetries are calculated with and without the long-distance contributions. Our numerical results for the nonresonant branching ratios for and B{sub c{yields}}D(D{sub s})l{sup +}l{sup -} are in the order of 10{sup -8} (10{sup -7}) and 10{sup -9} (10{sup -8}), respectively. The averaged values of the lepton polarization asymmetries obtained from the linear (harmonic oscillator) potential parameters are found to be -0.99 (-0.99) for B{sub c{yields}}D{mu}{sup +{mu}-} and -0.16 (-0.15) for B{sub c{yields}}D{tau}{sup +{tau}-}, and -0.98 (-0.98) for B{sub c{yields}}D{sub s{mu}}{sup +{mu}-} and -0.14 (-0.12) for B{sub c{yields}}D{sub s{tau}}{sup +{tau}-}, respectively.« less
  • We evaluate threshold resummed spectra in B{yields}X{sub u}l{nu} decays in next-to-leading order. We present results for the distribution in the hadronic variables E{sub X} and m{sub X}{sup 2}/E{sub X}{sup 2}, for the distribution in E{sub X} and for the distribution in E{sub X} and E{sub l}, where E{sub X} and m{sub X} are the total energy and the invariant mass of the final hadronic state X{sub u} respectively and E{sub l} is the energy of the charged lepton. We explicitly show that all these spectra (where there is no integration over the hadronic energy) can be directly related to themore » photon spectrum in B{yields}X{sub s}{gamma} via short-distance coefficient functions.« less
  • We resum to next-to-leading order the distribution in the ratio of the invariant hadron mass m{sub X} to the total hadron energy E{sub X} and the distribution in m{sub X} in the semileptonic decays B{yields}X{sub u}l{nu}. By expanding our formulas, we obtain the coefficients of all the infrared logarithms at O({alpha}{sub S}{sup 2}) and of the leading ones at O({alpha}{sub S}{sup 3}). We explicitly show that the relation between these semileptonic spectra and the photon spectrum in the radiative decay B{yields}X{sub s}{gamma} is not a purely short-distance one. There are long-distance effects in the semileptonic spectra which are not completelymore » factorized by the structure function as measured in the radiative decay and have to be modeled in some way.« less
  • We resum to next-to-leading order (NLO) the distribution in the light-cone momentum p{sub +}=E{sub X}-p-vector{sub X} and the spectrum in the electron energy E{sub e} in the semileptonic decays B{yields}X{sub u}l{nu}, where E{sub X} and p(vector sign){sub X} are the total energy and three-momentum of the final hadron state X{sub u} respectively. By expanding our formulae, we obtain the coefficients of all the infrared logarithms {alpha}{sub S}{sup n}L{sup k} at O({alpha}{sub S}{sup 2}) and at O({alpha}{sub S}{sup 3}), with the exception of the {alpha}{sub S}{sup 3}L coefficient. We explicitly show that the relation between these semileptonic spectra and the hadronmore » mass distribution in the radiative decay B{yields}X{sub s}{gamma} is not a purely short-distance one. By comparing our O({alpha}{sub S}{sup 2}n{sub f}) result for the p{sub +} distribution with a recent Feynman diagram computation, we obtain an explicit and nontrivial verification of our resummation scheme at the two-loop level (n{sub f} is the number of massless quark flavors). We also discuss the validity of the so-called Brodsky-Lepage-Mackenzie (BLM) scheme in the evaluation of the semileptonic spectra by comparing it with our results, finding that it is a reasonable approximation. Finally, we show that the long-distance phenomena, such as Fermi motion, are expected to have a smaller effect in the electron spectrum than in the hadron mass distribution.« less
  • We examine the anomalous dimension matrix appropriate for the phase space restricted B{yields}X{sub u}l{nu} and B{yields}X{sub s}{gamma} decay spectra to subleading nonperturbative order. The time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the nonlocal operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shapemore » functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of V{sub ub}.« less