Gauge Invariance and k_T-Factorization of Exclusive Processes

Abstract

In the $k_T$-factorization for exclusive processes, the nontrivial $k_T$-dependence of perturbative coefficients, or hard parts, is obtained by taking off-shell partons. This brings up the question of whether the $k_T$-factorization is gauge invariant. We study the $k_T$-factorization for the case $\pi {\gamma }^{\ast }\to \gamma$ at one-loop in a general covariant gauge. Our results show that the hard part contains a light-cone singularity that is absent in the Feynman gauge, which indicates that the $k_T$-factorization is {\it not} gauge invariant. These divergent contributions come from the $k_T$-dependent wave function of $\pi$ and are not related to a special process. Because of this fact the $k_T$-factorization for any process is not gauge invariant and is violated. Our study also indicates that the $k_T$-factorization used widely for exclusive B-decays is not gauge invariant and is violated.

Add some explanation, conclusion unchanged. Version to appear in PLB

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• Space-and Time-like Electromagnetic Kaon Form Factors
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• Study of ${\bar{B}}^0\to D^0{\mu }^{+}{\mu }^{-}$ Decay in Perturbative QCD Approach
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• Charmless $B_{u,d,s}\to VT$ decays in perturbative QCD approach
• Resummation of Large Logarithms in the Electromagnetic Form factor of pion
• A Note on the $k_T$-Factorization for Exclusive Processes