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

Abstract

We point out mistakes made in the one-loop calculation of some diagrams for the process $\pi {\gamma }^{\ast }\to \gamma$ 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.

Comments: 7 pages, 5 figures, a co-author was added, new method was adopted, the conclusion remains the same