Joint resummation for pion wave function and pion transition form factor

We construct an evolution equation for the pion wave function in the kT factorization formalism, whose solution sums the mixed logarithm ln x ln kT to all orders, with x (kT) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion wave function in the small x and large b regions, b being the impact parameter conjugate to kT, and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm ln2x and the conventional kT resummation for ln2kT. Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the γ*π0 → γ scattering, and to establish a scheme-independent kT factorization formula. It will be shown that the significance of next-to-leading-order contributions and saturation behaviors of this process at high energy differ from those under the conventional resummations. It implies that QCD logarithmic corrections to a process must be handled appropriately, before its data are used to extract a hadron wave function. Our predictions for the involved pion transition form factor, derived under the joint resummation and the input of a non-asymptotic pion wave function with the second Gegenbauer moment a2 = 0.05, match reasonably well the CLEO, BaBar, and Belle data.