Resummation of Large Logarithms in the Electromagnetic Form factor of pion

Abstract

In the collinear factorization of the form factor for the transition ${\gamma }^{\ast }{\pi }^0\to \pi$ the hard part contains double log terms. These terms will spoil the perturbative expansion of the hard part. A simple exponentiation for resummation leads to divergent results. We study the resummation of these double log's. We make an analysis to show the origin of the double log's. With the understanding of the origin one can introduce soft factors and Nonstandard Light-Cone Wave Functions(NLCWF) to derive a factorized form for the form factor, where the hard part does not contain the double log's. There is a perturbative relation between NLCWF and the standard Light-Cone Wave Function(LCWF). Beside the renormalization scale $\mu$ the introduced NLCWF's and soft factors have extra scales to characterize the double log's. Using the evolutions of the extra scales and the relation we can do the resummation of the double log's perturbatively in sense that LCWF's are the only nonpertubative objects in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with or without the resummation.

21 pages, 6 figures, title corrected

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