Transverse-Momentum Dependent Factorization for gamma^* pi^0 to gamma

Abstract

With a consistent definition of transverse-momentum dependent (TMD) light-cone wave function, we show that the amplitude for the process ${\gamma }^{\ast }{\pi }^0\to \gamma$ can be factorized when the virtuality of the initial photon is large. In contrast to the collinear factorization in which the amplitude is factorized as a convolution of the standard light-cone wave function and a hard part, the TMD factorization yields a convolution of a TMD light-cone wave function, a soft factor and a hard part. We explicitly show that the TMD factorization holds at one loop level. It is expected that the factorization holds beyond one-loop level because the cancelation of soft divergences is on a diagram-by-diagram basis. We also show that the TMD factorization helps to resum large logarithms of type ${\ln }^{2}x$.

Published version in Phys.Rev.D75:014014,2007

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• Resummation of Large Logarithms in ${\gamma }^{\ast }{\pi }^0\to \gamma$