Multi-particle production in proton-nucleus collisions in the Color Glass Condensate

TL;DR

This paper advances the calculation of multi-gluon production in proton-nucleus collisions within the Color Glass Condensate framework, incorporating quantum correlations and providing analytic results for two- and four-gluon cumulants.

Contribution

It extends previous models to include four-gluon production, develops a diagrammatic technique for color contractions, and generalizes the Wigner function approach to account for quantum correlations.

Findings

Second order four-particle cumulant is negative.

Correlations in the projectile significantly affect the results.

Analytic expressions for two-gluon cumulants are provided.

Abstract

We compute multi-gluon production in the Color Glass Condensate approach in dilute-dense collisions, p$A$, extending previous calculations up to four gluons. We include the contributions that are leading in the overlap area of the collision but keep all orders in the expansion in the number of colors. We develop a diagrammatic technique to write the numerous color contractions and exploit the symmetries to group the diagrams and simplify the expressions. To proceed further, we use the McLerran-Venugopalan and Golec-Biernat-W\"usthoff models for the projectile and target averages, respectively. We use a form of the Lipatov vertices that leads to the Wigner function approach for the projectile previously employed, that we generalise to take into account quantum correlations in the projectile wave function. We provide analytic expressions for integrated and differential two gluon cumulants and show a smooth dependence on the parameters defining the projectile and target Wigner function and dipole, respectively. For four gluon correlations we find that the second order four particle cumulant is negative, so a sensible second Fourier azimuthal coefficient can be defined. The effect of correlations in the projectile on this result results qualitatively and quantitatively large.