Thermal modification of bottomonium spectra from QCD sum rules with the maximum entropy method

TL;DR

This study uses QCD sum rules combined with the maximum entropy method to analyze bottomonium spectral functions at finite temperature, revealing the dissociation temperatures of various bottomonium states in hot QCD matter.

Contribution

It introduces a novel application of the maximum entropy method to QCD sum rules for extracting spectral functions without phenomenological models, providing new insights into bottomonium behavior at finite temperature.

Findings

Upsilon and  exteta_b survive up to 2.3T_c and 2.1T_c respectively.

 extchi_{b0} and extchi_{b1} dissociate below 2.5T_c.

Excited bottomonium states  extUpsilon(2S) and  extUpsilon(3S) dissociate at 1.5-2.0T_c.

Abstract

The bottomonium spectral functions at finite temperature are analyzed by employing QCD sum rules with the maximum entropy method. This approach enables us to extract the spectral functions without any phenomenological parametrization, and thus to visualize deformation of the spectral functions due to temperature effects estimated from quenched lattice QCD data. As a result, it is found that \Upsilon and \eta_b survive in hot matter of temperature up to at least 2.3T_c and 2.1T_c, respectively, while \chi_{b0} and \chi_{b1} will disappear at T<2.5T_c. Furthermore, a detailed analysis of the vector channel shows that the spectral function in the region of the lowest peak at T=0 contains contributions from the excited states, \Upsilon(2S) and \Upsilon(3S), as well as the ground states \Upsilon (1S). Our results at finite T are consistent with the picture that the excited states of bottomonia dissociate at lower temperature than that of the ground state. Assuming this picture, we find that \Upsilon(2S) and \Upsilon(3S) disappear at T=1.5-2.0T_c.