Bethe-Salpeter amplitudes of Upsilons

Based on lattice nonrelativistic QCD (NRQCD) studies, we present results for Bethe-Salpeter amplitudes for $\mathrm{\ensuremath{\Upsilon}}(1S)$, $\mathrm{\ensuremath{\Upsilon}}(2S)$, and $\mathrm{\ensuremath{\Upsilon}}(3S)$ in vacuum as well as in quark-gluon plasma. Our study is based on $2+1$ flavor ${48}^{3}\ifmmode\times\else\texttimes\fi{}12$ lattices generated using the Highly Improved Staggered Quark action and with a pion mass of 161 MeV. At zero temperature, the Bethe-Salpeter amplitudes follow the expectations based on nonrelativistic potential models. At nonzero 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.