Gauge invariance and kT-factorization of exclusive processes

In the kT-factorization for exclusive processes, the nontrivial kT-dependence of perturbative coefficients, or hard parts, is obtained by taking off-shell partons. This brings up the question of whether the kT-factorization is gauge invariant. We study the kT-factorization for the case πγ∗→γ at one-loop in a general covariant gauge. Our results show that the hard part contains a light-cone singularity that is absent in the Feynman gauge, which indicates that the kT-factorization is not gauge invariant. These divergent contributions come from the kT-dependent wave function of π and are not related to a special process. Because of this fact the kT-factorization for any process is not gauge invariant and is violated. Our study also indicates that the kT-factorization used widely for exclusive B-decays is not gauge invariant and is violated.