Evidence of collinear factorization breaking due to collinear-to-soft Glauber exchanges for a $2 \to 3$ exclusive process at leading twist

TL;DR

This paper demonstrates that collinear factorization breaks down in a specific exclusive photoproduction process due to Glauber gluon exchanges, leading to endpoint divergences at leading order.

Contribution

It provides the first explicit demonstration of collinear factorization breaking caused by Glauber gluons in a $2 o 3$ exclusive process at leading twist.

Findings

Glauber gluons cause endpoint divergences in the convolution integral.

Collinear factorization is violated in the studied process due to gluon exchange diagrams.

Glauber gluons are trapped by contour pinching, leading to factorization breaking.

Abstract

We exhibit an exclusive process, namely the photoproduction of a $\pi^{0}\gamma$ pair with large invariant mass, which violates collinear factorization. We explicitly demonstrate that this is due to the fact that there exists diagrams with gluon exchange in $t$ channel, contributing at the leading power, for which Glauber gluons are trapped. This is caused by the pinching of the contour integration of both the plus and minus light-cone components of the Glauber gluon momentum. We argue that this leads to the observed ``endpoint-like'' divergence of the convolution integral at leading order and leading power when collinear factorization is na\"ively assumed.