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.
Highlights
Potential models give a good description of the quarkonium spectrum below the open charm and bottom thresholds; see, e.g., Refs. [1,2] for reviews
Potential models can be justified using an effective field theory approach [3,4]. This approach is based on the idea that for a heavy quark with mass m, there is a separation of energy scales related to the quark mass, inverse size of the bound state, and binding energy, m ≫ mv ≫ mv2, with v being the velocity of the heavy quark inside the quarkonium bound state
Using lattice nonrelativistic QCD (NRQCD) in this paper, we studied the correlation functions, Crα, between operators optimized to have good overlaps with the of Υð1SÞ, Υð2SÞ, and Υð3SÞ vacuum wave functions and simple spatially nonlocal bottomonium operators, where the bottom quark and antiquark are separated by distance r
Summary
Potential models give a good description of the quarkonium spectrum below the open charm and bottom thresholds; see, e.g., Refs. [1,2] for reviews. One can reconstruct the potential from the Bethe-Salpeter amplitude [6,7,8,9,10] Most of these studies focused on quark masses close to or below the charm quark mass, though in Ref. One of our aims is to test the potential model by calculating the bottomonium Bethe-Salpeter amplitude using lattice NRQCD [11,12], which is very well suited for studying the bottomonium [13,14,15,16,17,18,19,20]. The existence and the properties of quarkonia in the hot medium attracted a lot of attention in the last 30 years It was proposed a long time ago that quarkonium production in heavy-ion collisions can be used to probe quark-gluon plasma formation [21].
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