Breakdown of collinear factorization in the exclusive photoproduction of a $ \pi ^{0}\gamma $ pair with large invariant mass

TL;DR

This paper demonstrates that collinear factorization breaks down in the exclusive photoproduction of a $b0 b0 b0$ pair with large invariant mass due to Glauber gluon effects, but remains valid for quark channels.

Contribution

It provides a detailed analysis showing factorization failure for gluon exchange processes while confirming validity for quark channels in exclusive photoproduction.

Findings

Glauber gluons cause factorization breakdown in gluon exchange channels.

Collinear factorization remains valid for quark exchange channels.

Processes with forbidden gluon exchanges are unaffected by the factorization issues.

Abstract

We study the exclusive photoproduction of a $ \pi ^{0}\gamma $ pair with large invariant mass $ M^{2}_{\gamma \pi} $, which is sensitive to the exchange of either two quarks or two gluons in the $ t $-channel. In this paper, we show that the process involving two-gluon exchanges does not factorize in the Bjorken limit at the leading twist. This can be explicitly demonstrated by the fact that there exist diagrams, which contribute at the leading twist, for which Glauber gluons are trapped, due to the pinching of the contour integration of both the plus and minus component of the Glauber gluon momentum. For the same reason, $\pi^0$-nucleon scattering to two photons also suffers from the same issue. On the other hand, we stress that there are no issues with respect to collinear factorization for the quark channels. By considering an analysis of all potential reduced diagrams of leading pinch-singular surfaces, we argue that the quark channel is safe from Glauber pinches, and therefore, a collinear factorization in that case follows through without any problems. This means that processes where gluon exchanges are forbidden, such as the exclusive photoproduction of $ \pi ^{\pm}\gamma $ and $ \rho^{0,\,\pm} \gamma $, are unaffected by the factorization breaking effects we point out in this paper.