Abstract
In this work, we strive to gain insight into thermal modifications of charmonium and bottomonium bound states as well as the heavy quark diffusion coefficient. The desired information is contained in the spectral function which can not be calculated on the lattice directly. Instead, the correlator given by an integration over the spectral function times an integration kernel is obtained. Extracting the spectral function is an ill-posed inversion problem and various different solutions have been proposed. We focus on a comparison to a spectral function obtained from combining perturbative and pNRQCD calculations. In order to get precise results, continuum extrapolated correlators originating from large and fine lattices are used. We first analyze the pseudoscalar channel since the absence of a transport peak simplifies the analysis. The knowledge gained from this is then used to extend the analysis to the vector channel, where information on heavy quark transport is encoded in the low frequency regime of the spectral function. The comparison shows a qualitatively good agreement between perturbative and lattice correlators. Quantitative differences can be explained by systematic uncertainties.
Highlights
Information on the in-medium properties like quarkonium bound states and heavy quark transport coefficients is contained in the spectral function
~x h(ψγi ψ)(τ, ~x )(ψγi ψ)(0,~0)ic. These correlators are related to the corresponding spectral functions through an integral equation, GPS,ii (τ ) =
Due to the structure of the integration kernel K (ω, τ ), the low frequency regime of the spectral function influences the shape of the correlator at larger τT while the high frequency part dominates the small distance part of the correlator
Summary
Information on the in-medium properties like quarkonium bound states and heavy quark transport coefficients is contained in the spectral function. Since the pseudoscalar channel does not contain a transport peak, it serves as an ideal probe for this comparison method. The knowledge obtained from pseudoscalar correlators can be used to extend the analysis to the vector channel. These correlators are related to the corresponding spectral functions through an integral equation, GPS,ii (τ ) =. Due to the structure of the integration kernel K (ω, τ ), the low frequency regime of the spectral function influences the shape of the correlator at larger τT while the high frequency part dominates the small distance part of the correlator. The transport peak complexifies the analysis and it is easier to test the method in the pseudoscalar channel, where no transport contribution is present, and use the gained knowledge for the vector channel analysis
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