Thermal QCD Research Articles

Monte-Carlo Simulation of Hard Probes in Heavy-Ion Collisions

Results from the Modular Algorithm for Relativistic Treatment of heavy IoN Interactions (MARTINI) are presented. This comprehensive event generator for the hard and penetrating probes in high energy nucleus-nucleus collisions employs a time evolution model for the soft background, PYTHIA 8.1 and the McGill-AMY parton evolution scheme including radiative as well as elastic processes. It generates full event configurations in the high pT region, taking into account thermal QCD and QED effects as well as effects of the evolving medium.

Next-to-leading order thermal spectral functions in the perturbative domain

Motivated by applications in thermal QCD and cosmology, we elaborate on a general method for computing next-to-leading order spectral functions for composite operators at vanishing spatial momentum, accounting for real, virtual as well as thermal corrections. As an example, we compute these functions (together with the corresponding imaginary-time correlators which can be compared with lattice simulations) for scalar and pseudoscalar densities in pure Yang-Mills theory. Our results may turn out to be helpful in non-perturbative estimates of the corresponding transport coefficients, which are the bulk viscosity in the scalar channel and the rate of anomalous chirality violation in the pseudoscalar channel. We also mention links to cosmology, although the most useful results in that context may come from a future generalization of our methods to other correlators.

Thermal QCD sum rules study of vector charmonium and bottomonium states

We calculate the masses and leptonic decay constants of the heavy vector quarkonia, $J/\psi$ and $\Upsilon$ mesons at finite temperature. In particular, considering the thermal spectral density as well as additional operators coming up at finite temperature, the thermal QCD sum rules are acquired. Our numerical calculations demonstrate that the masses and decay constants are insensitive to the variation of temperature up to $T\cong 100 ~MeV$, however after this point, they start to fall altering the temperature. At deconfinement temperature, the decay constants attain roughly to 45% of their vacuum values, while the masses are diminished about 12%, and 2.5% for $J/\psi$ and $\Upsilon$ states, respectively. The obtained results at zero temperature are in good consistency with the existing experimental data as well as predictions of the other nonperturbative models. Considerable decreasing in the values of the decay constants can be considered as a sign of the quark gluon plasma phase transition.

Theory of Heavy Flavor in the Quark-Gluon Plasma

Heavy-quark interactions in the Quark-Gluon Plasma are analyzed in terms of a selfconsistent Brueckner scheme using a thermodynamic $T$-matrix based on a potential model. The interrelations between quarkonium correlators, spectral functions and zero-modes, and open heavy-flavor transport and susceptibilities are elaborated. Independent constraints from thermal lattice QCD can be used to improve predictions for heavy-quark phenomenology in heavy-ion collisions.

Medium modifications and production of charmonia at LHC

A previously constructed transport approach to calculate the evolution of quarkonium yields and spectra in heavy-ion collisions is applied to PbPb (s=2.76A TeV) collisions at the Large Hadron Collider (LHC). In this approach spectral properties of charmonia are constrained by Euclidean correlators from thermal lattice QCD and subsequently implemented into a Boltzmann equation accounting for both suppression and regeneration reactions. Based on a fair description of SPS and RHIC data, we provide predictions for the centrality dependence of J/ψ yields at LHC. The main uncertainty is associated with the input charm cross section, in particular its hitherto unknown reduction due to shadowing in nuclear collisions. Incomplete charm-quark thermalization and non-equilibrium in charmonium chemistry entail a marked reduction of the regeneration yield compared to the statistical equilibrium limit.

Selfconsistent evaluation of charm and charmonium in the quark-gluon plasma

A selfconsistent calculation of heavy-quark (HQ) and quarkonium properties in the quark-gluon plasma (QGP) is conducted to quantify flavor transport and color screening in the medium. The main tool is a thermodynamic T-matrix approach to compute HQ and quarkonium spectral functions in both scattering and bound-state regimes. The T-matrix, in turn, is employed to calculate HQ selfenergies which are implemented into spectral functions beyond the quasiparticle approximation. Charmonium spectral functions are used to evaluate Eulcidean-time correlation functions, which are compared to results from thermal lattice QCD. The comparisons are performed in various hadronic channels, including zero-mode contributions consistently accounting for finite charm-quark width effects. The zero modes are closely related to the charm-quark number susceptibility, which is also compared to existing lattice ‘data’. Both the susceptibility and the heavy-light quark T-matrix are applied to calculate the thermal charm-quark relaxation rate, or, equivalently, the charm diffusion constant in the QGP. Implications of our findings in the HQ sector for the viscosity-to-entropy-density ratio of the QGP are briefly discussed.

Monte-Carlo simulation of heavy-ion collisions

We present Monte-Carlo simulations for heavy-ion collisions combining PYTHIA and the McGill-AMY formalism to describe the evolution of hard partons in a soft background, modelled using hydrodynamic simulations. MARTINI generates full event configurations in the high p T region that take into account thermal QCD and QED effects as well as effects of the evolving medium. This way it is possible to perform detailed quantitative comparisons with experimental observables.

Theory of Soft Electromagnetic Emission in Heavy-Ion Collisions

A status report of utilizing soft electromagnetic radiation (aka thermal photons and dileptons) in the diagnosis of strongly interacting matter in ultrarelativistic heavy-ion collisions is given. After briefly elaborating on relations of the electromagnetic spectral function to chiral symmetry restoration and the transition from hadron to quark degrees of freedom, various calculations of electromagnetic emission rates in the hadronic and quark-gluon plasma phases of QCD matter are discussed. This, in particular, includes insights from recent thermal lattice QCD computations. Applications to dilepton and photon spectra in heavy-ion collisions highlight their role as a spectro-, thermo-, baro- and chrono-meter of extraordinary precision.

QCD sum rules and thermal properties of Charmonium in the vector channel

The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J / ψ resonance mass, coupling (leptonic decay constant), total width, and continuum threshold is analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold s 0 , as in other hadronic channels, decreases with increasing temperature until the PQCD threshold s 0 = 4 m Q 2 is reached at T ≃ 1.22 T c ( m Q is the charm quark mass) and the J / ψ mass is essentially constant in a wide range of temperatures. The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The total width grows with temperature up to T ≃ 1.04 T c beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T ≃ T c . This behavior strongly suggests that the J / ψ resonance might survive beyond the critical temperature for deconfinement, in agreement with lattice QCD results.

On Bulk Viscosity and Moduli Decay

This pedagogically intended lecture, one of four under the header "Basics of thermal QCD", reviews an interesting relationship, originally pointed out by Bodeker, that exists between the bulk viscosity of Yang-Mills theory (of possible relevance to the hydrodynamics of heavy ion collision experiments) and the decay rate of scalar fields coupled very weakly to a heat bath (appearing in some particle physics inspired cosmological scenarios). This topic serves, furthermore, as a platform on which a number of generic thermal field theory concepts are illustrated. The other three lectures (on the QCD equation of state and the rates of elastic as well as inelastic processes experienced by heavy quarks) are recapitulated in brief encyclopedic form.

Quarkonia and heavy-quark relaxation times in the quark-gluon plasma

A thermodynamic T-matrix approach for elastic 2-body interactions is employed to calculate spectral functions of open and hidden heavy-quark systems in the Quark-Gluon Plasma. This enables the evaluation of quarkonium bound-state properties and heavy-quark diffusion on a common basis and thus to obtain mutual constraints. The two-body interaction kernel is approximated within a potential picture for spacelike momentum transfers. An effective field-theoretical model combining color-Coulomb and confining terms is implemented with relativistic corrections and for different color channels. Four pertinent model parameters, characterizing the coupling strengths and screening, are adjusted to reproduce the color-average heavy-quark free energy as computed in thermal lattice QCD. The approach is tested against vacuum spectroscopy in the open (D, B) and hidden (Psi and Upsilon) flavor sectors, as well as in the high-energy limit of elastic perturbative QCD scattering. Theoretical uncertainties in the static reduction scheme of the 4-dimensional Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are used to calculate Euclidean correlators which are discussed in light of lattice QCD results, while heavy-quark relaxation rates and diffusion coefficients are extracted utilizing a Fokker-Planck equation.

On heavy-quarkonia suppression by final-state multiple scatterings in most central Au + Au collisions at RHIC

We study heavy-quarkonia suppression under final-state multiple scatterings in most central Au + Au collisions at RHIC energy. We first calculate the survival probability of a heavy quarkonium under multiple scattering in Bjorken's expanding QGP at large N c . Then, we calculate the rapidity dependence of the nuclear modification factor R A A for heavy-quarkonia production by considering final-state multiple scatterings in most central Au + Au collisions in a simplified model. In our formula a constant P 0 is also introduced to estimate the possible cold nuclear effects. By fitting the data for J / Ψ production in most central Au + Au collisions at s N N = 200 GeV at RHIC, we find that the transportation coefficient q ˆ 0 ≃ ( 0.33 – 0.95 ) GeV 2 / fm , and, accordingly, the energy density at τ 0 is ϵ 0 ≃ ( 1.39 – 5.62 ) GeV / fm 3 in perturbative thermal QCD. A better understanding of cold nuclear effects is essential for us to get a more accurate analysis. The small values of the transportation coefficient q ˆ 0 in our estimate are in sharp contrast with those obtained by the analysis of high- p T hadron spectra in Eskola et al. (2005) [31].

Toward largeNthermal QCD from dual gravity: The heavy quarkonium potential

We continue our study on the gravity duals for strongly coupled large N QCD with fundamental flavors both at zero and non-zero temperatures. The gravity dual at zero temperature captures the logarithmic runnings of the coupling constants at far IR and the almost conformal, albeit strongly coupled, behavior at the UV. The full UV completion of gauge theory is accomplished in the gravity side by attaching an AdS cap to the IR geometry described in our previous work. Attaching such an AdS cap is highly non-trivial because it amounts to finding the right interpolating geometry and sources that take us from a gravity solution with non-zero three-form fluxes to another one that has almost vanishing three-form fluxes. In this paper we give a concrete realisation of such a scenario, completing the program advocated in our earlier paper. One of the main advantage of having such a background, in addition to providing a dual description of the required gauge theory, is the absence of Landau poles and consequently the UV divergences of the Wilson loops. The potential for the heaviest fundamental quark anti-quark pairs, which are like the heavy quarkonium states in realistic QCD, can be computed and their linear behavior at large separations and zero temperature could be demonstrated. At small separations the expected Coulombic behavior appears to dominate. On the other hand, at non-zero temperatures interesting properties like heavy quarkonium type suppressions and melting are shown to emerge from our gravity dual. We provide some discussions of the melting temperature and compare our results with the Charmonium spectrum and lattice simulations. We argue that, in spite of the large N nature of our construction, certain model-independent predictions can be made.

Properties of charmonia in a hot equilibrated medium

We investigate the properties of charmonia in a thermal medium, showing that with increasing temperature the decay widths of these mesons behave in a nontrivial way. Our analysis is based on a potential model with interaction potential extracted from thermal lattice QCD calculations of the free-energy of a static quark-antiquark pair. We find that in the crossover region some decay widths are extremely enhanced. In particular, at temperatures T ~ T c the decay widths of the J /Ψ that depend on the value of the wave function at the origin are enhanced with respect to the values in vacuum by about a factor 2. In the same temperature range the decay width of the process XcJ → J /Ψ + γ is enhanced by approximately a factor 6 with respect to the value in vacuum. At higher temperatures the charmonia states dissociate and the widths of both decay processes become vanishing small.

Leptonic decay constants of D s and B s mesons at finite temperature

In the present work, Ds and Bs meson parameters are investigated in the framework of thermal QCD sum rules. The temperature dependences of the mass and the leptonic decay constants are investigated by using Borel transform sum rules and Hilbert moment sum rules. To increase the sensitivity, the vacuum contributions are subtracted from the thermal expressions and the temperature dependences of the leptonic decay constants and meson masses are studied.

Heavy quark medium polarization at next-to-leading order

We compute the imaginary part of the heavy quark contribution to the photon polarization tensor, i.e. the quarkonium spectral function in the vector channel, at next-to-leading order in thermal QCD. Matching our result, which is valid sufficiently far away from the two-quark threshold, with a previously determined resummed expression, which is valid close to the threshold, we obtain a phenomenological estimate for the spectral function valid for all non-zero energies. In particular, the new expression allows to fix the overall normalization of the previous resummed one. Our result may be helpful for lattice reconstructions of the spectral function (near the continuum limit), which necessitate its high energy behaviour as input, and can in principle also be compared with the dilepton production rate measured in heavy ion collision experiments. In an appendix analogous results are given for the scalar channel.

Thermal QCD sum rules for σ(600) meson

In the present work, the temperature dependence of the scalar meson parameters is investigated in the framework of thermal QCD sum rules. We calculate the σ-pole and the non-resonant two-pion continuum contributions to the spectral density. Taking into account additional operators appearing at finite temperature, the thermal QCD sum rules are derived. The temperature dependence of the shifts in the mass and leptonic decay constant of the scalar σ(600) meson is calculated.

Thermal properties of heavy-light quark pseudoscalar and vector mesons

The thermal behaviour of the mass, leptonic decay constant, and width of heavy-light quark peseudoscalar and vector mesons is analized in the framework of thermal Hilbert moment QCD sum rules. In all the cases, the meson leptonic decay constants decrease with increasing T , and vanish at a critical temperature Tc, while the mesons develop a width which increases dramatically, diverging when T ! Tc, where Tc is the temperature for chiral-symmetry restoration. The spectral function becomes a smooth function of the energy. This is interpreted as a signal for deconfinement at T = Tc. In contrast, the thermal masses are stable, except when T ! Tc, where the pseudoscalar meson mass increases slightly by 10-20 %, and the vector meson mass decreases by some 20-30 %.

Shock waves from heavy-quark mesons in AdS/CFT

We calculate the far-field stress-energy tensor of a quark gluon plasma due to a heavy-quark meson moving through it, using a semi-classical description in string theory of the meson as a string hanging into anti-de Sitter space. We find that these mesons create a shock wave but no diffusion wake, in contrast to single heavy quarks described via a trailing string, where the diffusion wake is strong. If thermal QCD responds similarly to heavy quarks and heavy quarkonia, the presence or suppression of the diffusion wake constitutes a prediction which can in principle be checked in heavy-ion collisions.

Nonperturbative Heavy-Quark Diffusion in the Quark-Gluon Plasma

We evaluate heavy-quark (HQ) transport properties in a quark-gluon plasma (QGP) within a Brueckner many-body scheme employing interaction potentials extracted from thermal lattice QCD. The in-medium T matrices for elastic charm- and bottom-quark scattering off light quarks in the QGP are dominated by attractive meson and diquark channels which support resonance states up to temperatures of ~1.5T(c). The resulting drag coefficient increases with decreasing temperature, contrary to expectations based on perturbative QCD scattering. Employing relativistic Langevin simulations we compute HQ spectra and elliptic flow in sqrt[s(NN)]=200 GeV Au-Au collisions. A good agreement with electron decay data supports our nonperturbative computation of HQ diffusion, indicative for a strongly coupled QGP.