Quarkonium at finite temperature: towards realistic phenomenology from first principles

Abstract

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 Re[V ] with a single temperature dependent parameter m D , the Debye screening mass, and confirm the up to now tentative values of Im [V ]. The obtained analytic expression for the complex potential allows us to compute quarkonium spectral functions by solving an appropriate Schrödinger 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 (Re [V ]) and scattering (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.

In-medium P-wave quarkonium from the complex lattice QCD potential

“…This does not mean that in the spectral function no peak structure is visible anymore. On the contrary, when investigating S-wave quarkonium states in [1] we found that the remnant of the former bound state peak can survive to much higher temperatures after melting, according to the above criterium, has occurred. I.e.…”

“…Even though a Bayesian reconstruction is neccesary at this point, the Wilson line spectrum is much simpler than the two-body QQ spectrum itself [63] and can be robustly determined with currently available methods and simulation data sets [64]. 1 In the following we deploy the latest determination of the in-medium modification of the static complex in-medium potential from dynamical lattice QCD as in our previous S-wave study in ref. [1].…”

“…1 In the following we deploy the latest determination of the in-medium modification of the static complex in-medium potential from dynamical lattice QCD as in our previous S-wave study in ref. [1].…”

“…As the quarkonium correlator is related to its spectral function via a Fourier transform, we solve its Schrödinger equation directly in frequency space [72]. The computation is performed directly in Minkowski spacetime, without the need for an analytic continuation at this step and the resulting spectra 1 In fact the spectral function of the potential contains one dominant peak and falls off quickly at large and small frequencies so that the corresponding Euclidean correlator, i.e. the Coulomb gauge Wilson lines, is finite at τ = 0 also in the continuum [65][66][67].…”

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Abstract: We extend our lattice QCD potential based study [1] of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature.

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