Next-to-leading-order corrections to exclusive processes in k T factorization

We calculate next-to-leading-order corrections to exclusive processes in the kT factorization theorem, taking �� � ! � as an example. Partons off shell by k 2 are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kT-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms ln 2 kT and ln 2 x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the kT resummation and the latter absorbed into a jet function and organized by the threshold resummation. The next-to-leading-order corrections are found to be only a few percent for �� � ! � , if setting the factorization scale to the momentum transfer from the virtual photon.