Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop

Understand

We propose a non-perturbative and gauge invariant derivation of the static potential between a heavy-quark ($Q$) and an anti-quark ($\bar{Q}$) at finite temperature.

• This proper potential is defined through the spectral function (SPF) of the thermal Wilson loop and can be shown to satisfy the Schr\"{o}dinger equation for the heavy $Q\bar{Q}$ pair in the thermal medium.
• In general, the proper potential has a real and an imaginary part,corresponding to the peak position and width of the SPF.
• The validity of using a Schr\"{o}dinger equation for heavy $Q\bar{Q}$ can also be checked from the structure of the SPF.