Forward trijet production in proton-nucleus collisions: gluon initiated channel

TL;DR

This paper calculates the forward trijet production cross section in proton-nucleus collisions within the CGC framework, revealing new structures in gluon interactions and divergences relevant for NLO accuracy.

Contribution

It provides the first detailed analysis of the gluon-initiated trijet production, including novel insights into four-gluon vertex contributions and divergence structures.

Findings

Identified the four-gluon vertex topology similar to instantaneous contributions.

Connected rapidity divergence to JIMWLK evolution of color correlators.

Linked collinear divergences to evolution of gluon PDFs and fragmentation functions.

Abstract

In this paper, we present the results for the forward trijet production differential cross section in the gluon initiated channel at leading order in proton-nucleus collisions. The calculations are carried out within the Color Glass Condensate (CGC) effective theory, and in the dilute-dense approximation, using effective vertices for the quark and gluon propagators interacting with the small-$x$ background gluon field. We employ the covariant perturbation theory approach and disentangle the amplitudes into regular and instantaneous contributions. Our results are expressed as convolutions of multiparton color correlators of light-like Wilson lines and perturbative impact factors, organized in compact expressions in terms of the ``bare" topologies of the contributing diagrams. The gluon initiated channel receives contributions from a $q\bar{q}g$ and a $ggg$ final state. Interestingly, when considering the $ggg$ final state, we observe, for the first time, that the four-gluon vertex topology follows a structure similar to the instantaneous contributions. Furthermore, when integrating (one of) the real gluon(s) in the final state, we identify that: i) the rapidity divergence contributes to the real part of JIMWLK of the leading-order color correlator; and ii) the collinear divergence contribute to the evolution of initial-state gluon parton distribution function, and final state fragmentation functions. These results validate the dilute-dense hybrid formalism at one-loop order, and are key ingredients towards the complete next-to-leading order calculation of dijet/dihadron production in proton--nucleus collisions.