Long-Range Correlations between Observables in a Model with Translational Invariance in Rapidity

Vladimir Vechernin,Svetlana Belokurova

doi:10.3390/sym12071107

Abstract

We estimate the impact of the fixation of the total number of sources (quark–gluon strings) on the long-range rapidity correlations between different observables. In our approach this condition models the fixation of the collision centrality class, what is the usual practice in modern collider experiments, like Relativistic Heavy Ion Collider (RHIC), Large Hadron Collider (LHC) and so on. The estimates are obtained under the assumption of the translational invariance in rapidity, which is usually assumed in mid-rapidity region at high energies. Based on these assumptions, we are developing a technique for the analytical calculation of various average values of extensive and intense variables at high string densities on the transverse lattice, taking into account the effects of string fusion, leading to the formation of string clusters. Using this technique we calculate the asymptotes of the correlations coefficients both between the multiplicities and between the multiplicity and the event-mean transverse momentum of particles in two separated rapidity intervals. As a result, we found that fixing the total number of strings has a significant effect on the behavior of both types of correlations, especially in the case of a uniform distribution of strings in the transverse plane.

Highlights

In modern particle physics, one of the urgent tasks is to extract information about the initial stage of high-energy hadronic interactions
We present in details the developed methods for the analytical calculation of various average values of extensive and intensive variables at high string densities on the transverse lattice, what was announced in our short note [34], published as the proceedings of the WPCF Conference
We present the developed technique for the analytical calculation of various average values of extensive and intensive variables at high string densities on the transverse lattice with taking into account the string fusion effects leading to the formation of string clusters

Summary

Introduction

One of the urgent tasks is to extract information about the initial stage of high-energy hadronic interactions. The valuable source of such information can be the experimental and theoretical studies of the long-range correlations (LRCs) between observables in two separated rapidity windows usually refereed as forward (F) and backward (B) [1] In this approach one suggests that at the initial stage of the strong interaction at high energy the formation of boost invariant flux tubes of color fields take place between colliding hadrons. The estimates are obtained under the assumption of validity of the translational (boost) invariance in rapidity, which is usually assumed in the central rapidity region for symmetric reactions at high energies This assumption implies the uniform rapidity distribution of multiplicity and the dependence of the two-particle correlation function C2 (y1 , y2 ) only on the difference ∆y = y1 − y2 of the particle rapidities y1 and y2 [24].

The Model with the String Fusion on a Transverse Lattice

Averaging over String Configurations

Calculation of the Long-Range Correlation Coefficients

Summary