Quarkonium at finite temperature: Towards realistic phenomenology from first principles

TL;DR

This study computes the finite temperature spectra of bottomonium and charmonium using lattice QCD, revealing sequential melting and the effects of screening and scattering on quarkonium states.

Contribution

It introduces a lattice QCD based potential approach with a complex in-medium potential to analyze quarkonium spectral functions at finite temperature.

Findings

Confirmed the complex potential's imaginary part values.

Derived melting temperatures for different quarkonium states.

Observed spectral shifts due to screening and scattering effects.

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 ${\rm Re}[V]$ 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.