Bethe-Salpeter amplitudes of Upsilons

TL;DR

This study computes Bethe-Salpeter amplitudes of Upsilons using lattice NRQCD, revealing their behavior in vacuum and quark-gluon plasma, and compares results with potential models and previous lattice studies.

Contribution

First lattice NRQCD calculation of Upsilon Bethe-Salpeter amplitudes in vacuum and quark-gluon plasma, providing insights into their temperature dependence.

Findings

Amplitudes follow potential model expectations at zero temperature.

Non-zero temperature amplitudes show nuanced behavior consistent with previous studies.

Results support the understanding of Upsilon states in quark-gluon plasma.

Abstract

Based on lattice non-relativistic QCD (NRQCD) studies we present results for Bethe-Salpeter amplitudes for $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ in vacuum as well as in quark-gluon plasma. Our study is based on 2+1 flavor $48^3 \times 12$ lattices generated using the Highly Improved Staggered Quark (HISQ) action and with a pion mass of $161$ MeV. At zero temperature the Bethe-Salpeter amplitudes follow the expectations based on non-relativistic potential models. At non-zero temperatures, the interpretation of Bethe-Salpeter amplitudes turns out to be more nuanced, but consistent with our previous lattice QCD study of excited Upsilons in quark-gluon plasma.