# Insight into thermal modifications of quarkonia from a comparison of continuum-extrapolated lattice results to perturbative QCD$^{\dagger}$

## TL;DR

This paper compares continuum-extrapolated lattice QCD results with perturbative calculations to understand thermal effects on quarkonium states and heavy quark diffusion, highlighting qualitative agreement and systematic uncertainties.

## Contribution

It provides a detailed comparison between lattice and perturbative spectral functions for quarkonia at finite temperature, improving understanding of their thermal modifications.

## Key findings

- Qualitative agreement between lattice and perturbative correlators.
- Systematic uncertainties account for quantitative differences.
- Analysis extends from pseudoscalar to vector channels for transport insights.

## 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.