Abstract
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.
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Li, Hn., Shen, YL. & Wang, YM. Joint resummation for pion wave function and pion transition form factor. J. High Energ. Phys. 2014, 4 (2014). https://doi.org/10.1007/JHEP01(2014)004
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DOI: https://doi.org/10.1007/JHEP01(2014)004