Triple- and Quadruple-Gluon Azimuthal Correlations from Glasma and Higher-Dimensional Ridges

TL;DR

This paper calculates higher-order gluon correlations in the gluon saturation regime using glasma diagrams, predicting complex ridge structures in small collision systems at the LHC, and compares these with experimental data to understand the origin of collectivity.

Contribution

It introduces calculations of triple- and quadruple-gluon azimuthal correlations in the gluon saturation regime, extending beyond double-gluon correlations to clarify the origin of collectivity.

Findings

Reproduces systematics of p-p and p-Pb ridge data

Predicts higher-dimensional ridges in unmeasured correlations

Uses unintegrated gluon distributions from BK evolution

Abstract

We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating the long-range rapidity correlations ("ridges") and $v_n$ moments of the azimuthal distribution of detected hadrons. The glasma description reproduces the systematics of the data on both p-p and p-Pb ridges. As an alternative, relativistic hydrodynamics has also been applied to these small systems quite successfully. With the triple- and quadruple-gluon azimuthal correlations, this work aims to set the stage by going beyond the double-gluon azimuthal correlations in order to settle unambiguously the origin of "collectivity" in p-p and p-Pb collisions. We derive the triple- and quadruple-gluon azimuthal correlation functions in terms of unintegrated gluon distributions at arbitrary rapidities and azimuthal angles of the produced gluons. Then, unintegrated gluon distributions from the running coupling Balitsky-Kovchegov evolution equation are used to calculate the triple- and quadruple-gluon correlations for various parameters of gluon momenta, initial scale for small-$x$ evolution and beam energy.