Perturbative QCD factorization of πγ*->γ(π) and B->γ(π)lbar ν

We prove the factorization theorem for the processes πγ*->γ and πγ*->π to leading twist in the covariant gauge by means of the Ward identity. Soft divergences cancel and collinear divergences are grouped into a pion wave function defined by a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed. The proof is then extended to the exclusive B meson decays B->γl bar ν and B->πl bar ν in the heavy quark limit. It is shown that a light-cone B meson wave function, though absorbing soft dynamics, can be defined in an appropriate frame. Factorization of the B->πl bar ν decay in kT space, kT being parton transverse momenta, is briefly discussed. We comment on the extraction of the leading-twist pion wave function from experimental data