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.
Download