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B-meson light-cone distribution amplitude: Perturbative constraints and asymptotic behavior in dual space

Thorsten Feldmann* and Björn O. Lange†

Yu-Ming Wang‡

  • Theoretische Elementarteilchenphysik, Universität Siegen, 57068 Siegen, Germany

  • Institut für Theoretische Physik E, RWTH Aachen, 52056 Aachen, Germany; Technische Universität München, Physik Department, 85747 Garching, Germany

  • *thorsten.feldmann@uni-siegen.de
  • †lange@tp1.physik.uni-siegen.de
  • ‡yuming.wang@tum.de
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Phys. Rev. D 89, 114001 – Published 2 June, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.114001

Abstract

Based on the dual representation in terms of the recently established eigenfunctions of the evolution kernel in heavy-quark effective theory, we investigate the description of the B-meson light-cone distribution amplitude (LCDA) beyond tree level. In particular, in dual space, small and large momenta do not mix under renormalization, and therefore perturbative constraints from a short-distance expansion in the parton picture can be implemented independently from nonperturbative modelling of long-distance effects. It also allows us to (locally) resum perturbative logarithms from large dual momenta at fixed values of the renormalization scale. We construct a generic procedure to combine perturbative and nonperturbative information on the B-meson LCDA and compare different model functions and the resulting logarithmic moments which are the relevant hadronic parameters in QCD factorization theorems for exclusive B-meson decays.

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  24. If the hadronic model under consideration gives an explicit reference to the renormalization scale μ0, one would have to replace μ0→μω′(μ0) in ρmodel(ω′,μ0).

  25. In this paper we do not entertain the idea to change the mass scheme in the perturbative matching procedure itself. Although a renormalon-free scheme like the one proposed in [3] would improve the perturbative convergence for the regularized moments Mn, we do not expect a significant effect for the logarithmic moments relevant for phenomenological applications since, as we will show below, the contributions from the perturbative regime are subdominant there.

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Phys. Rev. D 89, 114001– Published 2 June, 2014
  • Received 14 April 2014

© 2014 American Physical Society

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