Quarkonium Spectral Functions Research Articles

Charmonium and bottomonium spectral functions in the vector channel

In this paper we report our results on quarkonium spectral functions in the vector channel obtained from quenched lattice QCD simulations at T ∈ [0.75,2.25] Tc. The calculations have been performed on very large and fine isotropic lattices where both charm and bottom quarks can be treated relativistically. The spectral functions are reconstructed using the Maximum Entropy Method. We study the dissociation of quarkonium states from the temperature dependence of the spectral functions and estimate heavy quark diffusion coefficients using the low-frequency behavior of the vector spectral functions.

Quarkonium at finite temperature: towards realistic phenomenology from first principles

We present the finite temperature spectra of both bottomonium and charmonium, obtained from a consistent lattice QCD based potential picture. Starting point is the complex in-medium potential extracted on full QCD lattices with dynamical u,d and s quarks, generated by the HotQCD collaboration. Using the generalized Gauss law approach, vetted in a previous study on quenched QCD, we fit ${\rm Re}[V]$ with a single temperature dependent parameter $m_D$, the Debye screening mass, and confirm the up to now tentative values of ${\rm Im}[V]$. The obtained analytic expression for the complex potential allows us to compute quarkonium spectral functions by solving an appropriate Schr\"odinger equation. These spectra exhibit thermal widths, which are free from the resolution artifacts that plague direct reconstructions from Euclidean correlators using Bayesian methods. In the present adiabatic setting, we find clear evidence for sequential melting and derive melting temperatures for the different bound states. Quarkonium is gradually weakened by both screening (${\rm Re}[V]$) and scattering (${\rm Im}[V]$) effects that in combination lead to a shift of their in-medium spectral features to smaller frequencies, contrary to the mass gain of elementary particles at finite temperature.

Modification of hadronic spectral functions under extreme conditions: An approach based on QCD sum rules and the maximum entropy method

Studies of quarkonium spectral functions at finite temperature, based on an approach combining QCD sum rules and the maximum entropy method are briefly reviewed. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. The maximum entropy method then allows us to obtain the most probable spectral function from the sum rules, without having to introduce any specific assumption about its functional form. Our findings suggest that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T_c, while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T_c or higher for S-wave and up to about 2.0 T_c for P-wave states.

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature Tc, while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 Tc or higher for S-wave and about 2.0 Tc for P-wave states.

Quarkonium spectral functions with complex potential

We study quarkonium spectral functions at high temperatures using a potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leads to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures slightly above 450 MeV.

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.

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.

Properties of quark gluon plasma from lattice calculations

I discuss lattice QCD calculations of the properties of strongly interacting matter at finite temperature, including the determination of the transition temperature Tc, equation of state, different static screening lengths and quarkonium spectral functions. The lattice data suggest that at temperatures above 2.0Tc many properties of the quark gluon plasma can be understood using weak coupling approach, although non-perturbative effects due to static magnetic fields are significant in some quantities.

Color Screening Melts Quarkonium

We calculate quarkonium spectral functions in a quark-gluon plasma using a potential model based on full QCD lattice calculations of the free energy of a static quark-antiquark pair. We estimate the binding energy and the thermal width of different quarkonium states. The estimated upper limit for the dissociation temperatures is considerably lower than the ones suggested in the recent literature.

Ground State Quarkonium Spectral Functions above Deconfinement

We discuss the temperature-dependence of S-wave quarkonium spectral functions in a nonrelativistic Green's function approach and compare these to lattice QCD results.