Bottonium in QCD at finite temperature

TL;DR

This study investigates the behavior of bottomonium states at finite temperature using thermal QCD sum rules, revealing their stability in mass but significant changes in decay properties near the critical temperature.

Contribution

It provides the first detailed analysis of vector and pseudoscalar bottomonium states at finite temperature within the thermal Hilbert moment QCD sum rules framework, highlighting their thermal stability.

Findings

Mass and $s_0$ show little temperature dependence.

Width and decay constant exhibit strong temperature dependence.

Bottomonium states likely survive above the critical temperature.

Abstract

Vector ($\Upsilon$) and pseudoscalar ($\eta_b$) bottonium ground states are studied at finite temperature in the framework of thermal Hilbert moment QCD sum rules. The mass, the onset of perturbative QCD in the complex squared energy plane, $s_0$, the leptonic decay constant, and the total width are determined as a function of the temperature. Results in both channels show very little temperature dependence of the mass and of $s_0$, in line with expectations. However, the width and the leptonic decay constant exhibit a very strong $T$-dependence. The former increases with increasing temperature, as in the case of light- and heavy-light-quark systems, but close to the critical temperature, $T_c$, and for $T/T_c \simeq 0.9$ it drops dramatically approaching its value at T=0, as obtained recently in this framework for charmonium states. The leptonic decay constant is basically a monotonically increasing function of the temperature, also as obtained in the charmonium channel . These results are interpreted as the survival of these bottonium states above $T_c$, in line with lattice QCD results.