Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-07-02
Phys.Lett.B674:176-181,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
Add some explanation, conclusion unchanged. Version to appear in PLB
Scientific paper
10.1016/j.physletb.2009.02.060
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 $\pi \gamma^* \to \gamma$ 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.
Feng Feng
Ma Jian-Ping
Wang Qiangguo
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