B-Meson Wavefunction in the Wandzura-Wilczek Approximation

Abstract

The B-meson wavefunction has been studied with the help of the vacuum-to-meson matrix element of the nonlocal 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 ${\omega }_0=2\bar{\Lambda }$, the solutions for the B-meson wavefunction in this paper agree well with the one obtained by directly taking the heavy quark limit $m_b\to \infty$. 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 ${\Psi }_{\pm }(\omega ,z^2)$. Based on the obtained results, we claim that both its distribution amplitudes ${\varphi }_B(\omega )$ and ${\bar{\varphi }}_B(\omega )$ are important for calculating the B meson decays.

Comments: 12 pages, 2 figures