Heavy quarkonium in any channel in resummed hot QCD

TL;DR

This paper models quarkonium in hot QCD as a transient state with an imaginary potential, analyzing spectral functions and dilepton rates across temperatures, revealing that resonance peaks diminish but quark contributions increase with temperature.

Contribution

It introduces a Schrödinger equation approach with an imaginary potential to study quarkonium spectral functions in hot QCD, highlighting the persistence of resonance features and their impact on dilepton production.

Findings

Resonance peaks in spectral functions diminish with temperature.

Scalar channel resonance can be observed in bottomonium.

Dilepton rate contributions from quarkonium increase with temperature.

Abstract

We elaborate on the fact that quarkonium in hot QCD should not be thought of as a stationary bound state in a temperature-dependent real potential, but as a short-lived transient, with an exponentially decaying wave function. The reason is the existence of an imaginary part in the pertinent static potential, signalling the ``disappearance'', due to inelastic scatterings with hard particles in the plasma, of the off-shell gluons that bind the quarks together. By solving the corresponding Schr\"odinger equation, we estimate numerically the near-threshold spectral functions in scalar, pseudoscalar, vector and axial vector channels, as a function of the temperature and of the heavy quark mass. In particular, we point out a subtlety in the determination of the scalar channel spectral function and, resolving it to the best of our understanding, suggest that at least in the bottomonium case, a resonance peak can be observed also in the scalar channel, even though it is strongly suppressed with respect to the peak in the vector channel. Finally, we plot the physical dilepton production rate, stressing that despite the eventual disappearance of the resonance peak from the corresponding spectral function, the quarkonium contribution to the dilepton rate becomes more pronounced with increasing temperature, because of the yield from free heavy quarks.