Multi-particle production in proton\u2013nucleus collisions in the color glass condensate

Pedro Agostini,Néstor Armesto,Tolga Altinoluk

doi:10.1140/epjc/s10052-021-09475-0

Abstract

We compute multi-gluon production in the Color Glass Condensate approach in dilute-dense collisions, hbox {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–Wüsthoff 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.

Highlights

Small collision systems, proton-proton and proton-nucleus, studied at the Large Hadron Collider (LHC) show many of the characteristics [1,2,3,4,5] that in heavy ion collisions are considered as signatures of the formation of hot deconfined partonic matter, the Quark Gluon Plasma
The open questions at this moment are how the conditions for hydrodynamics to be applicable are reached from an initial state that is very far from equilibrium [27] – the emergence of the macroscopic description given by hydrodynamics from Quantum Chromodynamics (QCD), for which both strong and weak coupling explanations have been proposed, and why hydrodynamics seems to work even for large anisotropies, outside its presumed range of applicability
Where ξ 2 is a parameter with dimensions of momentum squared. This choice, it does not maintain some important properties of the Lipatov vertices, it is much simpler to deal with and, as we show in Appendix C, it is equivalent to using the Wigner function approach [44,45,64,65,94] but including quantum correlations in the projectile wave function

Summary

Introduction

Proton-proton ( pp) and proton-nucleus ( pA), studied at the Large Hadron Collider (LHC) show many of the characteristics [1,2,3,4,5] that in heavy ion collisions are considered as signatures of the formation of hot deconfined partonic matter, the Quark Gluon Plasma. The most prominent example is the existence of azimuthal correlations in the two-particle inclusive distributions that are extended in pseudorapidity and show maxima when the particle transverse momenta are either parallel or antiparallel This finding, named the ridge, was first observed in high multiplicity pp collisions [6], and for smaller multiplicities [7,8,9,10], in pPb collisions [11,12,13,14,15,16] and in association with Z boson production [17]. In heavy ion collisions where the partonic density is very large, a natural explanation is that collectivity is built through the strong final state interactions of the created system Such explanation looks justified by the success of viscous relativistic hydrodynamics [25,26] for describing the observed experimental features in soft particle production. Hydrodynamics appears as the effective theory for describing the soft modes of any field theory, see e.g. [29] and references therein

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Results

Conclusion