Next-to-leading-order calculation in kT factorization

We explain the framework for calculating next-to-leading-order （NLO） corrections to exclusive processes in the kT factorization theorem, taking πγ^＊→γ as an example. Patrons off-shell by kT^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 kw-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms In^2 kT and In^2x, 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 the latter into a jet function.