Joint resummation for pion wave function and pion transition form factor

We construct an evolution equation for the pion wave function in the k _T factorization formalism, whose solution sums the mixed logarithm ln x ln k _T to all orders, with x ( k _T ) 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 k _T , 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 ln² x and the conventional k _T resummation for ln² k _T . Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the γ ^* π ⁰ → γ scattering, and to establish a scheme-independent k _T 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 a ₂ = 0 .05, match reasonably well the CLEO, BaBar, and Belle data.