Evolution of initial stage fluctuations in the glasma

Pablo Guerrero-Rodríguez,Tuomas Lappi

doi:10.1103/physrevd.104.014011

Abstract

We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general four-point function of the initial color fields. Our results provide analytical insight into the preequilibrium phase of heavy ion collisions without requiring a numerical solution to the Yang-Mills equations.

Highlights

Heavy ion collisions (HICs) open an experimental window to the most extreme regimes of quantum chromodynamics (QCD)
We have presented an analytical calculation of one- and two-point correlators of energy density and axial charge at finite proper times
These objects characterize the average and fluctuations of energy density and axial charge deposited throughout the initial stage of HICs, during which a classical description of the system is appropriate

Summary

INTRODUCTION

Heavy ion collisions (HICs) open an experimental window to the most extreme regimes of quantum chromodynamics (QCD). The magnitude of such fluctuations is encoded in the following difference of correlators: Sfðx⊥; y⊥Þ 1⁄4 hfðx⊥Þfðy⊥Þi − hfðx⊥Þihfðy⊥Þi; ð1Þ where fðx⊥Þ denotes the value of a property of the glasma at a point x⊥ of the transverse plane and the notation h...i represents an average over the background fields Such correlations have been computed analytically in previous works for both the energy density [17,18,19] and the axial charge [8,18,20] deposited by the nuclei right after the collision (i.e., for an infinitesimal positive proper time τ 1⁄4 0þ). In Appendix C, we briefly discuss the results obtained under the MV model with a fixed coupling constant

INITIAL CONDITIONS

The MV model

PROPER TIME EVOLUTION

One-point functions

Two-point functions

CONCLUSIONS