Relation between light cone distribution amplitudes and shape function in B mesons

Journal Article · Fri Feb 01 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.034005· OSTI ID:21039020

Le Yaouanc, A; Oliver, L; Raynal, J -C ^[1]

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1. Laboratoire de Physique Theorique Universite de Paris XI, Batiment 210, 91405 Orsay Cedex (France)

The Bakamjian-Thomas relativistic quark model provides a Poincare representation of bound states with a fixed number of constituents and, in the heavy quark limit, form factors of currents satisfy covariance and Isgur-Wise scaling. We compute the light cone distribution amplitudes (LCDA) of B mesons {phi}{sub {+-}}{sup B}({omega}) as well as the shape function S({omega}), that enters in the decay B{yields}X{sub s}{gamma}, that are also covariant in this class of models. The LCDA and the shape function are related through the quark model wave function. The former satisfy, in the limit of vanishing constituent light quark mass, the integral relation given by QCD in the valence sector of Fock space. Using a Gaussian wave function, the obtained S({omega}) is identical to the so-called roman shape function. From the parameters for the latter that fit the B{yields}X{sub s}{gamma} spectrum we predict the behavior of {phi}{sub {+-}}{sup B}({omega}). We discuss the important role played by the constituent light quark mass. In particular, although {phi}{sub -}{sup B}(0){ne}0 for vanishing light quark mass, a nonvanishing mass implies the unfamiliar result {phi}{sub -}{sup B}(0)=0. Moreover, we incorporate the short distance behavior of QCD to {phi}{sub +}{sup B}({omega}), which has sizeable effects at large {omega}. We obtain the values for the parameters {lambda} congruent with 0.35 GeV and {lambda}{sub B}{sup -1} congruent with 1.43 GeV{sup -1}. We compare with other theoretical approaches and illustrate the great variety of models found in the literature for the functions {phi}{sub {+-}}{sup B}({omega}); hence the necessity of imposing further constraints as in the present paper. We briefly review also the different phenomena that are sensitive to the LCDA. The value that we find for {lambda}{sub B}{sup -1} fulfills the upper bound recently measured by BABAR.

• OSTI ID: 21039020
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 3 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
B MESONS
B QUARKS
BOUND STATE
C QUARKS
COMPARATIVE EVALUATIONS
D QUARKS
DISTRIBUTION
FORM FACTORS
GEV RANGE
LIGHT CONE
PHOTONS
QUANTUM CHROMODYNAMICS
QUARK MODEL
RELATIVISTIC RANGE
T QUARKS
U QUARKS
VALENCE
WAVE FUNCTIONS