The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The r-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length r. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of mDr, where mD is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential shows little sensitivity to the lattice spacing at small mDr ≲ 1 and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.

$$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

Exact Green’s function of photon and medium effects in QED2+1

In (2+1)­-dimensional Maxwell­-Chern­-Simons quantum electrodynamics, we derive the structure of the exact polarization operator in the presence of medium characterized by a chemical potential μ. We show that the transverse part of the operator is the sum of four tensors. These tensors and unit one form an algebra with respect to the commutation operation. Green’s function of photons at zero temperature is derived on the basis of calculations of the one­loop form factors. The spectrum of modes is investigated. We find that the transverse and longitudinal modes exist in medium. This result differs from that of other authors. Dependence of the photon Debye mass on the form factors is investigated and a static electric potential is calculated.

Thermal corrections to the gluon magnetic Debye mass

We compute the gluon polarization tensor in a thermo-magnetic environment in thestrong magnetic field limit at zero and high temperature. The magnetic field effects are introduced using Schwinger's proper time method. Thermal effects are computed in the HTL approximation. At zero temperature, we reproduce the well-known result whereby for a non-vanishing quark mass, the polarization tensor reduces to the parallel structure and its coefficient develops an imaginary part corresponding to the threshold for quark-antiquark pair production. This coefficient is infrared finite and simplifies considerably when the quark mass vanishes. Keeping always the field strength as the largest energy scale, in the high temperature regime we analyze two complementary hierarchies of scales: $q^2<< m_f^2<< T^2$ and $m_f^2<< q^2<< T^2$. In the latter, we show that the polarization tensor is infrared finite as $m_f$ goes to zero. In the former, we discuss the thermal corrections to the magnetic Debye mass.

Dense quark–gluon plasma in strong magnetic fields

A non-perturbative (np) method of Field correlators (FCM) was applied to study QCD at temperatures above the deconfinement transition ($$1<T/T_c<3,~T_c\sim 0.16~\mathrm{GeV}$$1<T/Tc<3,Tc∼0.16GeV) and nonzero baryon densities (baryon chemical potential $$\mu _B<0.5~\mathrm{GeV}$$μB<0.5GeV) in an external uniform magnetic field ($$eB<0.5~\mathrm{GeV}^2$$eB<0.5GeV2). Within FCM, the np high-temperature dynamics is embodied in the Polyakov loop and in the Debye mass due to the Color-Magnetic confinement. Analytic expressions for quark pressure and magnetic susceptibility were obtained. The expressions were represented as series and in integral form. Magnetic susceptibility was found to increase rapidly with temperature and slowly with density. The results at the zero density limit are in agreement with lattice data.

Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

By using the conformable fractional of the Nikiforov–Uvarov (CF–NU) method, the radial Schrödinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on the heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher-dimensional space. This paper discusses the flavor dependence of their binding energies and explores the nature of dissociation by employing the perturbative, nonperturbative, and the lattice-parametrized form of the Debye masses in the medium-modified potential. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D with consideration of a form of the Debye mass.

Equation of States and Charmonium Suppression in Heavy-Ion Collisions

The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as an equation of state. By employing medium modification to a heavy quark potential thermodynamic observables, viz., pressure, energy density, speed of sound, etc. have been calculated which nicely fit with the lattice equation of state for gluon, massless, and as well massive flavored plasma. For obtaining the thermodynamic observables we employed the debye mass in the quasi particle picture. We extended the quasi-particle model to calculate charmonium suppression in an expanding, dissipative strongly interacting QGP medium (SIQGP). We obtained the suppression pattern for charmonium states with respect to the number of participants at mid-rapidity and compared it with the experimental data (CMS JHEP) and (CMS PAS) at LHC energy (Pb+Pb collisions, sNN = 2.76 TeV).

Quarkonium Phenomenology from a Generalised Gauss Law

We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass m D . Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the Ψ ′ / J / Ψ ratio in heavy-ion collisions at different beam energies.