Gluon splitting in a shockwave
Edmond Iancu, Julien Laidet
TL;DR
This work develops a CGC-based calculation of forward di-gluon production in proton–nucleus collisions, deriving the $gA\to ggX$ cross-section in the leading-log high-energy limit. The partonic amplitude includes two time-orderings of the gluon splitting relative to the shockwave, and the cross-section is expressed in terms of multi-Wilson-line correlators that encode initial- and final-state interactions. In the large-$N_c$ limit, the result reduces to dipole- and quadrupole-based structures, enabling connections to BK evolution and unintegrated gluon distributions; the analysis of dilute, back-to-back, and DPS regimes reveals saturation effects and geometric scaling persist even for relatively hard final-state gluons. The work also clarifies how to handle DPS contributions and provides a framework to compare CGC predictions with k_T- and TMD-factorization, with potential implications for interpreting forward-rapidity data at the LHC.
Abstract
The study of azimuthal correlations in particle production at forward rapidities in proton-nucleus collisions provides direct information about high gluon density effects, like gluon saturation, in the nuclear wavefunction. In the kinematical conditions for proton-lead collisions at the LHC, the forward di-hadron production is dominated by partonic processes in which a gluon from the proton splits into a pair of gluons, while undergoing multiple scattering off the dense gluon system in the nucleus. We compute the corresponding cross-section using the Colour Glass Condensate effective theory, which enables us to include the effects of multiple scattering and gluon saturation in the leading logarithmic approximation at high energy. This opens the way towards systematic studies of angular correlations in two-gluon production, similar to previous studies for quark-gluon production in the literature. We consider in more detail two special kinematical limits: the "back-to-back correlation limit", where the transverse momenta of the produced gluons are much larger than the nuclear saturation momentum, and the "double parton scattering limit", where the two gluons are produced by a nearly collinear splitting occurring prior to the collision. We argue that saturation effects remain important even for relatively high transverse momenta (i.e. for nearly back-to-back configurations), leading to geometric scaling in the azimuthal distribution.