Gauge Invariance and k_T-Factorization of Exclusive Processes

TL;DR

This paper investigates the gauge invariance of $k_T$-factorization in exclusive processes, revealing that it is not gauge invariant due to light-cone singularities, which challenges its widespread use in B-decay analyses.

Contribution

The study demonstrates that $k_T$-factorization is not gauge invariant in exclusive processes, highlighting the presence of divergences in general covariant gauges.

Findings

Light-cone singularity in the hard part in covariant gauges

$k_T$-factorization is not gauge invariant

Violation of $k_T$-factorization in exclusive B-decays

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 $\pi \gamma^* \to \gamma$ 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.