# Transport in the Gluon Plasma

**Principal Investigator:** Dr. Dénes Sexty, Heisenberg Fellow, Bergische Universität Wuppertal (Germany)

**HPC Platform:** JUQUEEN of JSC

Ordinary matter consists of electrons and nuclei, with the nuclei being composed of neutrons and protons, and the protons and the neutrons being composed of quarks and gluons. One of the fundamental questions in subatomic physics is what happens to matter at high densities and/or temperatures which prevailed in the first microseconds after the Big Bang and which might still prevail in the core of neutron stars. At these extreme conditions it is expected that quarks and gluons freely propagate over large distances, in contrast to ordinary matter where the quarks and gluons are confined inside of protons and neutrons. This state of matter is often called the quark gluon plasma (QGP). Relativistic heavy ion collider experiments at facilities like the Large Hadron Collider (LHC) at CERN, the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven, and the future Facility for Antiproton and Ion Research (FAIR) at GSI are designed to give us some insight about matter at such extreme conditions.

It is widely accepted, that the physics of heavy ion collisions is described by the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). However, QCD is an extremely challenging theory to solve, especially for non-equilibrium processes, and therefore theorists must resort to phenomenological descriptions. One of the most important of these is relativistic hydrodynamics.

The relativistic hydrodynamic description of the heavy ion collision goes back to Landau’s work in the year 1953, even before QCD was invented. Interest in relativistic hydrodynamics grew in the mid-2000s, when it turned out that experimental results at the Relativistic Heavy-Ion Collider (RHIC) are described very well by an almost perfect fluid description. In technical terms this means that the viscosity of the produced medium is low. The viscosity of a fluid is a measure of its resistance to deformation by shear stress, and a low viscosity is a signal for strong interactions between the microscopic constituents of the fluid. This experimental finding led to many interesting theoretical and phenomenological investigations. While it is established that these collisions create a strongly coupled liquid, we do not know the precise nature of the initial state from which this liquid forms, and know very little about how the properties of this liquid vary across its phase diagram or how, at a microscopic level, the collective properties of this liquid emerge from the interactions among the individual quarks and gluons [1].

In particular it is known for a while that the applicability of hydrodynamics does not imply local thermal equilibirum, as there are many examples of model systems, when even a far from equilibirum system admits a hydrodynamic prescription [2]. It is an important question then if the phenomenological value of the viscosity coincides with the equilibrium value of the viscosity or not. To settle this question a crucial missing ingredient is the calculation of the equilibrium viscosity of the QGP.

It is well established, that QCD near the crossover temperature is a strongly coupled system, and the only well-established, systematically improvable, first principle calculation tool for such a system in lattice QCD. The lattice QCD calculation of the viscosity is very difficult however, since the mathematical description of the calculation involves a so-called inverse problem, similar to de-blurring an image. To be able to estimate the viscosity, an unprecedented precision is needed for the related lattice observables, the correlations of the energy-momentum tensor. This high precision was the main goal and also the main challenge of this project, with the caveat that for the moment we stick to a theory slightly simpler than QCD, pure Yang-Mills theory, a theory of only gluons and no quarks.

To achieve this high precision statistics simulations of pure Yang-Mills theory have been performed, with state-of-the-art algorithms, leading to a sub-percent precision on the related observables. It was also shown that previous determinations of these observables [3-4] suffered from undetermined discretization error on the order of a few percent, making the estimates unreliable just by this fact alone. Nevertheless the estimated value of the viscosity to entropy-density ratio remains in the same ballpark as in those earlier studies.

Copyright: University of Wuppertal

**External References**

[1] Akiba, Yasuyuki et al, The Hot QCD White Paper: Exploring the Phases of QCD at RHIC and the LHC, arXiv:1502.02730 [nucl-ex]

[2] P. Romatschke, Do nuclear collisions create a locally equilibrated quark–gluon plasma?, Eur.Phys.J. C77 (2017) no.1, 21, arXiv:1609.02820 [nucl-th]

[3] H. B. Meyer, A Calculation of the shear viscosity in SU(3) gluodynamics, Phys.Rev. D76 (2007) 101701, arXiv:0704.1801 [hep-lat]

[4] N. Astrakhantsev et al, Temperature dependence of shear viscosity of SU(3) -- gluodynamics within lattice simulation, JHEP 1704 (2017) 101, arXiv:1701.02266 [hep-lat]

**Scientific Contact:**

Dr. Dénes Sexty

Institut für Theoretische Teilchenphysik

Fakultät für Mathematik und Naturwissenschaften

Bergische Universität Wuppertal, D-42097 Wuppertal (Germany)

e-mail: sexty [at] uni-wuppertal.de

*October 2017*