Heavy quark medium polarization at next-to-leading order

TL;DR

This paper calculates the heavy quark contribution to the photon polarization tensor at next-to-leading order in thermal QCD, providing a spectral function estimate useful for lattice QCD and heavy ion collision analysis.

Contribution

It presents a next-to-leading order computation of the heavy quark spectral function, bridging near-threshold and high-energy regimes for the first time.

Findings

Derived a spectral function valid for all energies.

Fixed the normalization of previous resummed results.

Provided results applicable to lattice QCD and experimental data.

Abstract

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.