Lattice NRQCD study of S- and P-wave bottomonium states in a thermal medium with $N_f=2+1$ light flavors

TL;DR

This study uses lattice QCD and a novel Bayesian method to analyze bottomonium states near the deconfinement transition, revealing that certain states survive at high temperatures and providing insights into medium modifications.

Contribution

It introduces a new Bayesian approach for spectral function extraction that outperforms the maximum entropy method in finite temperature lattice QCD studies.

Findings

1 state persists up to 249 MeV.

The new Bayesian method reliably detects ground state signals.

Constraints on medium modifications of bottomonium states.

Abstract

We investigate the properties of S-and P-wave bottomonium states in the vicinity of the deconfinement transition temperature. The light degrees of freedom are represented by dynamical lattice QCD configurations of the HotQCD collaboration with $N_f = 2 + 1$ flavors. Bottomonium correlators are obtained from bottom quark propagators, computed in nonrelativistic quantum chromodynamics (NRQCD) under the background of these gauge field configurations. The spectral functions for the $^3S_1$ ($\Upsilon$) and $^3P_1$ ($\chi_{b1}$) channel are extracted from the Euclidean time correlators using a novel Bayesian approach in the temperature region $140 {\rm MeV} \le T \le 249 {\rm MeV}$ and the results are contrasted to those from the standard maximum entropy method. We find that the new Bayesian approach is far superior to the maximum entropy method. It enables us to study reliably the presence or absence of the lowest state signal in the spectral function of a certain channel, even under the limitations present in the finite temperature setup. We find that $\chi_{b1}$ survives up to $T=249 {\rm MeV}$, the highest temperature considered in our study and put stringent constraints on the size of the medium modification of $\Upsilon$ and $\chi_{b1}$ states.