Transverse Momentum Distribution in the B Mesons in the Heavy-quark Limit: the Wandzura-Wilczek Part

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In the heavy-quark limit, the valence Fock-state components in the B mesons are described by a set of two light-cone wavefunctions. We show that these two wavefunctions obey simple coupled differential equations, which are based on the equations of motion in the Heavy Quark Effective Theory (HQET), and the analytic solutions for them are obtained. The results generalize the recently obtained longitudinal-momentum distribution in the Wandzura-Wilczek approximation by including the transverse momenta. We find that the transverse momentum distribution depends on the longitudinal momentum of the constituents, and that the wavefunctions damp very slowly for large transverse separation between quark and antiquark.