Double inclusive small- x gluon production and their azimuthal correlations in a biased ensemble

Gary Kapilevich

doi:10.1103/physrevd.101.034035

Abstract

We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal correlations, for a few simple examples of biases.

Highlights

Observables in particle collision experiments are often evaluated in biased event ensembles
One may consider a class of events with greater than average multiplicity of produced particles, or events with high transverse energy deposition in a particular rapidity window, and so on
DNi d2 kdy refers to the transverse momentum distribution of particles in event i, and dNmb d2 kdy is the average over all events

Summary

INTRODUCTION

Observables in particle collision experiments are often evaluated in biased event ensembles. We relate expectation values in biased ensembles in high-energy collisions to reweighted averages over the field configurations of small-x gluons in the colliding particles. That our approach allows us to compute expectation values in an ensemble defined by a functional bias on the gluon distribution Xðk⃗ Þ, rather than an ensemble defined with a bias on gluon number, mean transverse momentum, etc. We recompute the so-called “glasma graphs” for a biased gluon distribution different from its expectation value XsðkÞ in the unbiased small-x ensemble. These diagrams for high-pT double gluon production have originally been introduced in Refs. II, we write the two gluon inclusive distribution at high

TWO GLUON INCLUSIVE DISTRIBUTION IN A BIASED ENSEMBLE

SPECIFIC ENSEMBLES

E Þ2bΘðQ2

Transverse momentum dependent boost of the gluon density

E Þ2 : ð65Þ

SUMMARY AND CONCLUSION