B-meson wave function with contributions from three-particle Fock states

Abstract

The $B$-meson light-cone wave functions, ${\ensuremath{\Psi}}_{\ifmmode\pm\else\textpm\fi{}}(\ensuremath{\omega},{z}^{2})$, are investigated up to the next-to-leading order in Fock state expansion in the heavy-quark limit. In order to know the transverse momentum dependence of the $B$-meson wave functions with 3-particle Fock states' contributions, we make use of the relations between 2- and 3- particle wave functions derived from the QCD equations of motion and the heavy-quark symmetry, especially two constraints derived from the gauge field equation of motion are employed. Our results show that the use of gluon equation of motion can give a constraint on the transverse momentum dependence $\ensuremath{\chi}(\ensuremath{\omega},{\mathbf{k}}_{\ensuremath{\perp}})$ of the $B$-meson wave functions, whose distribution tends to be a hyperbolalike curve under the condition $0<{c}_{1}<1$, which is quite different from the Wandzura-Wilczek-(WW)-type wave functions, whose transverse momentum dependence ${\ensuremath{\chi}}^{\mathrm{WW}}(\ensuremath{\omega},{\mathbf{k}}_{\ensuremath{\perp}})$ is merely a delta function. Based on the derived results, we propose a simple model for the $B$-meson wave functions with 3-particle Fock states' contributions.