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The transport and spectral properties of heavy quarkonia in hot QCD matter are a central ingredient to describe their observables in high-energy heavy-ion collisions. We review recent activity in evaluating these properties, including a nonperturbative quantum many-body approach where the basic two-body interaction kernel is constrained by quantities that can be computed with good precision in thermal lattice QCD. We then give a brief overview of quarkonium transport approaches to heavy-ion collisions. Focusing on the semiclassical approach we discuss the current interpretation of charmonium and bottomonium observables at RHIC and the LHC, including excitation functions that started with 𝐽/𝜓 and 𝜓′ data from the heavy-ion program at the SPS. 

The electric conductivity, ${\sigma }_{\mathrm{el}}$, is a fundamental transport coefficient of QCD matter that can be related to the zero-energy limit of the electromagnetic (EM) spectral function at vanishing three-momentum in the medium. The EM spectral function is also the central quantity to describe the thermal emission rates and pertinent spectra of photon and dilepton radiation in heavy-ion collisions. Employing a model for dilepton rates that combines hadronic many-body theory with nonperturbative QGP emission constrained by lattice QCD which describes existing dilepton measurements in heavy-ion collisions, I investigate the sensitivity of low-mass dilepton spectra in Pb-Pb collisions at the CERN Large Hadron Collider (LHC) to ${\sigma }_{\mathrm{el}}$. In particular, I separately evaluate the contributions from QGP and hadronic emission, and identify signatures that can help to extract ${\sigma }_{\mathrm{el}}$from high-precision experimental data expected to be attainable with future detector systems at the LHC. Published by the American Physical Society2024 

The invariant mass spectra of dileptons radiated from the fireballs formed in high-energy heavy-ion collisions have been successfully used to investigate the properties of hot and dense QCD matter. Using a realistic model for the in-medium electromagnetic spectral function, we predict polarization observables and compare them to experiment. This allows, for the first time, independent tests of the longitudinal and transverse components of the virtual photon’s selfenergy. While the low- and high-mass regions exhibit the expected limits of transverse and unpolarized photons, respectively, baryon-driven medium effects in the 𝜌-meson mass region create a marked longitudinal polarization that transits into a largely unpolarized emission from the quark-gluon plasma, thus providing a sensitive test of microscopic emission processes in QCD matter. Applications to available data from the HADES and NA60 experiments at SIS and SPS energies, respectively, are consistent with our predictions and set the stage for quantitative polarization studies at FAIR and collider energies. 

We provide an update on our semi-classical transport approach for quarkonium production in high-energy heavy-ion collisions, focusing on J/ψ and ψ(2S) mesons in 5.02 TeV Pb-Pb collisions at the Large Hadron Collider (LHC) at both forward and mid-rapidity. In particular, we employ the most recent charm-production cross sections reported in pp collisions, which are pivotal for the magnitude of the regeneration contribution, and their modifications due to cold-nuclear-matter (CNM) effects. Multi-differential observables are calculated in terms of nuclear modification factors as a function of centrality, transverse momentum, and rapidity, including the contributions from feeddown from bottom hadron decays. For our predictions for ψ(2S) production, the mechanism of sequential regeneration relative to the more strongly bound J/ψ meson plays an important role in interpreting recent ALICE data. 

A previously constructed 𝑇-matrix approach for studying the quark-gluon plasma (QGP) is improved by incorporating spin-dependent interactions between partons. These interactions arise from the relativistic corrections to the Cornell potential. We first study the vacuum spectroscopy of quarkonia with this potential and find that a significant admixture of a vector component in the confining potential (rather than the previously considered scalar interaction) improves the description of the experimental mass splittings in 𝑆- and 𝑃-wave states. The in-medium potential containing the vector component in the confining interaction is constrained by fitting lattice-QCD results for heavy-quark (HQ) free energies and the equation of state (EoS) computed within in the selfconsistent 𝑇-matrix framework. We subsequently extract the transport coefficients for charm quarks in the QGP with the improved in-medium potentials. The relativistic corrections to the vector component of the confining potential cause a notable increase in the thermal relaxation rate of charm quarks in the QGP in comparison to previous calculations, especially at high momenta. These results are expected to have significant ramifications for the phenomenology of open heavy-flavor observables at RHIC and the LHC. 

The thermodynamicT-matrix approach is used to study Wilson line correlators (WLCs) for a static quark-antiquark pair in the quark-gluon plasma (QGP). Selfconsistent results that incorporate constraints from the QGP equation of state can approximately reproduce WLCs computed in 2+1-flavor lattice-QCD (lQCD), provided the input potential exhibits less screening than in previous studies. Utilizing the updated potential to calculate pertinent heavylightT-matrices we evaluate thermal relaxation rates of heavy quarks in the QGP. We find a more pronounced temperature dependence for low-momentum quarks than in our previous results (with larger screening), which turns into a weaker temperature dependence of the (temperature-scaled) spatial diffusion coefficient, in fair agreement with the most recent lQCD data. 

We extend a previously constructed T -matrix approach to the quark-gluon plasma (QGP) to include the effects of spin-dependent interactions between partons. Following earlier work within the relativistic quark model, the spin-dependent interactions figure as relativistic corrections to the Cornell potential. When applied to the vacuum spectroscopy of quarkonia, in particular their mass splittings in S- and P-wave states, the issue of the Lorentz structure of the confining potential arises. We confirm that a significant admixture of a vector interaction (to the previously assumed scalar interaction) improves the description of the experimental mass splittings. The temperature corrections to the in-medium potential are constrained by results from thermal lattice quantum chromodynamics for the equation of state and heavy-quark free energy in a self-consistent setup for heavyand light-parton spectral functions in the QGP. We then deploy the refined in-medium heavy-light T matrix to compute the charm-quark transport coefficients in the QGP. The vector component of the confining potential, through its relativistic corrections, enhances the friction coefficient for charm quarks in the QGP over previous calculations by tens of percentages at low momenta and temperatures and more at higher momenta. Our results are promising for improving the current phenomenology of open heavy-flavor observables at Relativistic Heavy Ion Collider and the Large Hadron Collider.