<p>We extend our investigation of heavy quark transport coefficients in the effective dynamical quasiparticle model (DQPM)—which reproduces nonperturbative QCD phenomena in the strongly interacting quark-gluon plasma according to lattice QCD data—by including inelastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo stretchy="false">→</mo><mn>3</mn></math> processes with massive gluon radiation, in addition to elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo stretchy="false">→</mo><mn>2</mn></math> parton scattering. Both elastic and inelastic reactions are evaluated at leading order using DQPM-based effective propagators and vertices, accounting for all channels and their interferences. Based on the obtained matrix elements, we calculate various observables connected to a charm quark. First, we calculate the total cross section of a charm quark with the medium partons as functions of temperature and collision energy. Second, we obtain the drag <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">A</mi></math> coefficient and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>q</mi><mo stretchy="false">^</mo></mover></math> coefficient of a charm quark as functions of temperature and momentum and also compare our results with those obtained using the Zakharov model for the momentum-dependent strong coupling for the elastic and radiative vertices with a heavy quark, highlighting the importance of the choice of the strong coupling in the determination of transport coefficients. Third, we calculate the spatial diffusion coefficient of a charm quark and compare our results with those obtained using other approaches. Finally, we explore the mass dependence of the diffusion coefficient by comparing the results for charm quark, bottom quark, and infinitely heavy quark. We found that inelastic processes can play a significant role in the determination of the transport coefficients at large transverse momenta, but are strongly suppressed at low transverse momenta.</p>

Germany

Ilia Grishmanovskii

Taesoo Song

Carsten Greiner

Elena Bratkovskaya

Transport coefficients of heavy quarks by elastic and radiative scatterings in the strongly interacting quark-gluon plasma

<p>We present a microscopic dynamical model to study the formation, dissociation, and recombination processes of charmonium states in a heat bath at constant temperature and volume. Within this classical approach, heavy quarks are described as Brownian particles in a background medium of light constituents and can therefore be modeled by a Fokker-Planck equation with constant transport coefficients, which is then implemented through relativistic Langevin simulations. The heavy quarks interact classically via a Coulomb-like screened potential to form a bound state if the relative energy of the pair becomes negative. Dissociation of bound states is possible as a result of screening effects on the potential as well as through scatterings with plasma particles. We demonstrate the full equilibration of the system and show that the resulting equilibrium charmonium yields are in accordance with the Statistical Hadronization Model.</p>

Naomi Oei

Nadja Krenz

Hendrik van Hees

Spain

Juan M. Torres-Rincon

Formation, dissociation, and regeneration of charmonia within microscopic Langevin simulations

We present realistic estimates for the duration of the hadronic stage in central Au+Au reactions in the RHIC-BES energy regime. To this aim, we employ a full set of coupled rate equations to describe the time evolution of the system from chemical to kinetic freeze-out. Combined with the recently measured data by the STAR collaboration on <math altimg='si1.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mo stretchy='false'>/</mo><mi>K</mi></math> ratios, we show that the previous estimates substantially underestimated the duration of this stage due to the omission of the regeneration of hadron resonances. We provide an improved relation between the <math altimg='si1.svg'><msup><mrow><mi>K</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup><mo stretchy='false'>/</mo><mi>K</mi></math> ratio at chemical and kinetic freeze-out and the life time of the hadronic phase. The calculated improved life times are now in line with estimates from other methods and are relevant for the NA61 and STAR collaborations and for upcoming experiments at the FAIR facility.

Tim Neidig

Thailand

Apiwit Kittiratpattana

Tom Reichert

Amine Chabane

Marcus Bleicher

Determining the duration of the hadronic stage at RHIC-BES energies via resonance suppression using a full set of rate equations

We present exact relations between the diffusion coefficients or conductivities, <math><mrow><msub><mi>κ</mi><mrow><mi>q</mi><msup><mi>q</mi><mo>′</mo></msup></mrow></msub><mo>/</mo><mi>T</mi><mo>=</mo><msub><mi>σ</mi><mrow><mi>q</mi><msup><mi>q</mi><mo>′</mo></msup></mrow></msub></mrow></math>, of strongly interacting matter. We show that once the diagonal entries are known in two different charge representations, the off-diagonal coefficients are functions of the diagonal entries once isospin symmetry applies. As an important example, we infer the conductivities on the basis of available calculations from lattice quantum chromodynamics and argue that these computations suffer under the approximations made to achieve them. Further, we argue that the representation of the conductivities with respect to the conserved quark flavors may deliver more insight into the chemical composition of strongly interacting matter.

Jan A. Fotakis

Jakob E. Lohr

Exact relations between the conductivities and their connection to the chemical composition of QCD matter

We extend the investigation of jet transport coefficients within the effective dynamical quasiparticle model (DQPM)—constructed to describe nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (sQGP) in line with the lattice QCD equation of state—by accounting for inelastic <math><mrow><mn>2</mn><mo>→</mo><mn>3</mn></mrow></math> reactions with gluon radiation in addition to the elastic scattering of partons. The elastic and inelastic reactions are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM by accounting for all channels and their interferences. We present the results for the jet transport coefficients such as the transverse momentum transfer squared <math><mover><mi>q</mi><mo>̂</mo></mover></math> per unit length as well as the energy loss <math><mrow><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></mrow></math> per unit length in the sQGP and investigate their dependence on the temperature <math><mi>T</mi></math> and momentum of the jet parton depending on the choice of the strong coupling constant <math><msub><mi>α</mi><mi>s</mi></msub></math> in thermal, jet parton, and radiative vertices. For the latter, we consider different scenarios used in the literature and find a very strong dependence of <math><mover><mi>q</mi><mo>̂</mo></mover></math> and <math><mrow><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></mrow></math> on the choice of <math><msub><mi>α</mi><mi>s</mi></msub></math>. Moreover, we explore the relation of <math><mrow><mover><mi>q</mi><mo>̂</mo></mover><mo>/</mo><msup><mi>T</mi><mn>3</mn></msup></mrow></math> to the ratio of specific shear viscosity to entropy density <math><mrow><mi>η</mi><mo>/</mo><mi>s</mi></mrow></math> and show that the ratio <math><mrow><msup><mi>T</mi><mn>3</mn></msup><mo>/</mo><mover><mi>q</mi><mo>̂</mo></mover></mrow></math> to <math><mrow><mi>η</mi><mo>/</mo><mi>s</mi></mrow></math> has a strong <math><mi>T</mi></math> dependence—especially when approaching <math><msub><mi>T</mi><mi>c</mi></msub></math>—on the choice of <math><msub><mi>α</mi><mi>s</mi></msub></math> in scattering vertices.

Olga Soloveva

Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma

We study the temporal evolution of quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles. For this open quantum system we formulate the non-equilibrium Kadanoff-Baym equations for the system particles by taking the interactions to be elastic 2-2 scatterings with the heat-bath particles. The corresponding spatially inhomogeneous integro-differential equations for the one-particle Greens's function are solved numerically. We demonstrate how the system particles equilibrate and thermalize with the heat bath and how the off-diagonal elements of the density matrix, expressed in the one-particle energy eigenbasis, decohere, so that only the diagonal entries, i.e. the occupation numbers, survive. In addition, the time evolution of the (retarded) Green's function also determines the spectral properties of the various one-particle quantum states.

Jan Rais

Open quantum systems with Kadanoff-Baym equations

We investigate the role of inelastic processes in the strongly interacting quark-gluon plasma (sQGP) based on the effective dynamical quasiparticle model (DQPM). In the DQPM the nonperturbative properties of the sQGP at finite temperature <math><mi>T</mi></math> and baryon chemical potential <math><msub><mrow><mo>μ</mo></mrow><mi>B</mi></msub></math> are described in terms of strongly interacting off-shell partons (quarks and gluons) with dynamically generated spectral functions whose properties are adjusted to reproduce the lattice QCD equation of state for the quark-gluon plasma in thermodynamic equilibrium. For the first time the massive gluon radiation processes from the off-shell quark-quark <math><mrow><mo>(</mo><mi>q</mi><mo>+</mo><mi>q</mi><mo>)</mo></mrow></math> and quark-gluon <math><mrow><mo>(</mo><mi>q</mi><mo>+</mo><mi>g</mi><mo>)</mo></mrow></math> scatterings are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM without any further approximations. We present the results for the energy and temperature dependencies of the total and differential radiative cross sections and compare them to the corresponding elastic cross sections. We show that our results reproduce the perturbative QCD calculations in the limit of zero masses and widths of quasiparticles. Also we study the μ<math><msub><mrow></mrow><mi>B</mi></msub></math> dependence of the inelastic cross sections. Moreover, we present estimates for the transition rate and relaxation time of radiative versus elastic scatterings in the sQGP.

Inelastic and elastic parton scattering in the strongly interacting quark-gluon plasma

The electromagnetic response of hot QCD matter to decaying external magnetic fields is investigated. We examine the validity of Ohm's law and find that the induced electric current increases from zero and relaxes towards the value from Ohm's law. The relaxation time is larger than the lifetime of the external magnetic field for the QCD matter in relativistic heavy-ion collisions. The lower-than-expected electric current significantly suppresses the induced magnetic field and makes the electromagnetic response incomplete. We demonstrate the incomplete electromagnetic response of hot QCD matter by calculations employing the parton transport model combined with the solution of Maxwell's equations. Our results show a strong suppression by two orders of magnitude in the magnetic field relative to calculations assuming the validity of Ohm's law. This may undermine experimental efforts to measure magnetic-field-related effects in heavy-ion collisions.

China

Zeyan Wang

Jiaxing Zhao

Zhe Xu

Pengfei Zhuang

Incomplete electromagnetic response of hot QCD matter

The creation of loosely bound objects in heavy ion collisions, e.g. light clusters, near the phase transition temperature (<math><msub><mrow><mi>T</mi></mrow><mrow><mi>ch</mi></mrow></msub><mo>≈</mo><mn>155</mn><mtext> MeV</mtext></math>) has been a puzzling observation that seems to be at odds with Big Bang nucleosynthesis suggesting that deuterons and other clusters are formed only below a temperature <math><mi>T</mi><mo>≈</mo><mn>0.1</mn><mo>−</mo><mn>1</mn><mtext> MeV</mtext></math>. We solve this puzzle by showing that the light cluster abundancies in heavy ion reactions stay approximately constant from chemical freeze-out to kinetic freeze-out. To this aim we develop an extensive network of coupled reaction rate equations including stable hadrons and hadronic resonances to describe the temporal evolution of the abundancies of light (anti-)(hyper-)nuclei in the late hadronic environment of an ultrarelativistic heavy ion collision. It is demonstrated that the chemical equilibration of the light nuclei occurs on a very short timescale as a consequence of the strong production and dissociation processes. However, because of the partial chemical equilibrium of the stable hadrons, including the nucleon feeding from Δ resonances, the abundancies of the light nuclei stay nearly constant during the evolution and cooling of the hadronic phase. This solves the longstanding contradiction between the thermal fits and the late stage coalescence (and the Big Bang nucleosynthesis) and explains why the observed light cluster yields are compatible with both a high chemical production temperature and a late state emission as modeled by coalescence. We also note in passing that the abundancies of the light clusters in the present approach are in excellent agreement with those measured by ALICE at LHC.

Kai Gallmeister

United States

Volodymyr Vovchenko

Towards solving the puzzle of high temperature light (anti)-nuclei production in ultra-relativistic heavy ion collisions

We study the diffusion properties of the strongly interacting quark-gluon plasma (sQGP) and evaluate the diffusion coefficient matrix for the baryon (B), strange (S) and electric (Q) charges—<math><msub><mi>κ</mi><mrow><mi>q</mi><msup><mi>q</mi><mo>′</mo></msup></mrow></msub></math> (<math><mrow><mi>q</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>B</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>Q</mi></mrow></math>) and show their dependence on temperature <math><mi>T</mi></math> and baryon chemical potential <math><msub><mi>μ</mi><mi>B</mi></msub></math>. The nonperturbative nature of the sQGP is evaluated within the dynamical quasiparticle model (DQPM) which is matched to reproduce the equation of state of the partonic matter above the deconfinement temperature <math><msub><mi>T</mi><mi>c</mi></msub></math> from lattice QCD. The calculation of diffusion coefficients is based on two methods: (i) the Chapman-Enskog method for the linearized Boltzmann equation, which allows to explore nonequilibrium corrections for the phase-space distribution function in leading order of the Knudsen numbers as well as (ii) the relaxation time approximation (RTA). In this work we explore the differences between the two methods. We find a good agreement with the available lattice QCD data in case of the electric charge diffusion coefficient (or electric conductivity) at vanishing baryon chemical potential as well as a qualitative agreement with the recent predictions from the holographic approach for all diagonal components of the diffusion coefficient matrix. The knowledge of the diffusion coefficient matrix is also of special interest for more accurate hydrodynamic simulations.