Abstract

To study the microscopic structure of quark–gluon plasma, data from hadronic collisions must be confronted with models that go beyond fluid dynamics. Here, we study a simple kinetic theory model that encompasses fluid dynamics but contains also particle-like excitations in a boost invariant setting with no symmetries in the transverse plane and with large initial momentum asymmetries. We determine the relative weight of fluid dynamical and particle like excitations as a function of system size and energy density by comparing kinetic transport to results from the 0th, 1st and 2nd order gradient expansion of viscous fluid dynamics. We then confront this kinetic theory with data on azimuthal flow coefficients over a wide centrality range in PbPb collisions at the LHC, in AuAu collisions at RHIC, and in pPb collisions at the LHC. Evidence is presented that non-hydrodynamic excitations make the dominant contribution to collective flow signals in pPb collisions at the LHC and contribute significantly to flow in peripheral nucleus–nucleus collisions, while fluid-like excitations dominate collectivity in central nucleus–nucleus collisions at collider energies.

Highlights

  • To set the stage for these questions, we recall that any self-interacting matter that does not spontaneously breakLorentz symmetry carries both fluid-dynamic and non-fluid dynamic excitations

  • Parton cascades have been used to study the Boltzmann transport equation in isolation with the aim of gaining qualitative insights into how kinetic theory approaches a hydrodynamic regime [24,26,34,35,36], how it builds up collective flow [37,38,39,40], and how this affects the flow of heavy quarks [41]

  • To ask what is the microscopic structure of quark–gluon plasma, is to ask how the plasma behaves away from the hydrodynamic limit

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Summary

Introduction

To set the stage for these questions, we recall that any self-interacting matter that does not spontaneously break. While experimental reality prevents us from directly measuring the response of a static and infinite quark–gluon plasma to a linearized perturbation and directly accessing the nonhydrodynamic structures, the non-hydrodynamic sector may leave its imprint to the dynamical evolution of the system created in physical collisions. With decreasing τ ∼ R, one may access an increasing amount of information about the nonhydrodynamic structures that lie deeper in the complex plane For both of these reasons, systems that are small enough are inevitably dominated by physics that is not fluid-like and the specific way of how the hydrodynamic description fails for small systems carries the information of what lies beyond. It is a natural starting point to ask how this limit is approached in the only one of the above mentioned models that does support free streaming, namely the kinetic theory

Background
The model
Isotropization-time approximation
Initial conditions
Numerical results
Time evolution of Tkμinν
Quantifying deviations of Tkμinν from fluid dynamics
Work in kinetic theory
Data comparison
The centrality dependence of opacity γ
Opacity γin PbPb at the LHC
Opacity γin pPb at the LHC
Opacity γin AuAu at RHIC
Data on pPb collisions at the LHC
Data for AuAu collisions at RHIC
Non-ideal equation of state
Non-linear response to spatial eccentricities
Centrality dependence of initial eccentricities 2 and
Reconstructing eccentricity for pPb collisions
Comment on measures of system size in small systems
Conclusions
Free-streaming variables
Scaling of the initial conditions and of the equations of motion
Findings
Numerical solution

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