B-Meson Wavefunction with Contributions from 3-particle Fock States

Abstract

The B-meson light-cone wavefunctions, $Ψ_{\pm}(ω,z^2)$, 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 wavefunctions with 3-particle Fock states' contributions, we make use of the relations between 2- and 3- particle wavefunctions 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 $χ(ω,\mathbf{k}_\perp)$ of the B-meson wavefunctions, whose distribution tends to be a hyperbola-like curve under the condition $0<c_1<1$, which is quite different from the WW type wavefunctions, whose transverse momentum dependence $χ^{WW}(ω,\mathbf{k}_\perp)$ is merely a delta function. Based on the derived results, we propose a simple model for the B-meson wavefunctions with 3-particle Fock states' contributions.