B-meson wavefunction in the Wandzura-Wilczek approximation

The B-meson wavefunction has been studied with the help of the vacuum-to-meson matrix element of the non-local operators in the heavy quark effective theory. In order to obtain the Wandzura-Wilczek-type B-meson wavefunction, we solve the equations which are derived from the equation of motion of the light spectator quark in the B meson by using two different assumptions. Under the condition that ω0=2Λ¯, the solutions for the B-meson wavefunction in this paper agree well with the one obtained by directly taking the heavy quark limit mb→∞. Our results show that the equation of motion of the light spectator quark in the B meson can impose a strong constraint on the B-meson wavefunctions Ψ±(ω,z2). Based on the obtained results, we claim that both its distribution amplitudes ϕB(ω) and ϕ¯B(ω) are important for calculating the B meson decays.