Comment on "Gauge Invariance and $k_T$-Factorization of Exclusive Processes"

TL;DR

This paper corrects previous one-loop calculations in a specific process, clarifies misconceptions about light-cone singularities, and demonstrates the gauge invariance of the hard kernel in $k_T$ factorization for exclusive processes.

Contribution

It provides corrected calculations, clarifies the nature of light-cone singularities, and confirms the gauge invariance of the hard kernel in $k_T$ factorization.

Findings

Corrected one-loop calculation results.

Disproved the existence of light-cone singularity from highly off-shell gluons.

Confirmed gauge invariance of the hard kernel in $k_T$ factorization.

Abstract

We point out mistakes made in the one-loop calculation of some diagrams for the process $\pi \gamma^* \to \gamma$ in the preprint arXiv:0807.0296, and present correct results. Especially, we have difficulty to understand their argument that a highly off-shell gluon generates a light-cone (infrared) singularity. It is shown by means of the Ward identity that the gauge-dependent light-cone singularity found in arXiv:0807.0296 does not exist. It is then shown that a hard kernel derived in the $k_T$ factorization of exclusive processes is gauge invariant and free of the light-cone singularity.