Abstract
We discuss, how to study $I = 0$ quarkonium resonances decaying into pairs of heavy-light mesons using static potentials from lattice QCD. These static potentials can be obtained from a set of correlation functions containing both static and light quarks. As a proof of concept we focus on bottomonium with relative orbital angular momentum $L = 0$ of the $\bar{b} b$ pair corresponding to $J^{P C} = 0^{- +}$ and $J^{P C} = 1^{- -}$. We use static potentials from an existing lattice QCD string breaking study and compute phase shifts and $\mbox{T}$ matrix poles for the lightest heavy-light meson-meson decay channel. We discuss our results in the context of corresponding experimental results, in particular for $\Upsilon (10860)$ and $\Upsilon (11020)$.
Highlights
A long-standing problem in QCD is to understand exotic hadrons, i.e., hadrons which have a structure more complicated than a mesonic quark-antiquark pair or a baryonic triplet of quarks [1]
As a proof of concept, we focus on bottomonium with relative orbital angular momentum LQQ 1⁄4 0 of the bb pair corresponding to JPC 1⁄4 0−þ and JPC 1⁄4 1−−
We show how to set up a corresponding coupled channel Schrödiger equation in a consistent way and explain how the potential matrix is related to static potentials from QCD, which can be computed with lattice QCD
Summary
A long-standing problem in QCD is to understand exotic hadrons, i.e., hadrons which have a structure more complicated than a mesonic quark-antiquark pair or a baryonic triplet of quarks [1]. The problem of identifying or predicting exotic hadrons, say tetraquarks, pentaquarks, hexaquarks, hybrids, or glueballs, turned out to be much harder than initially expected One approach to studying hadrons composed of heavy quarks and antiquarks as well as of gluons and possibly light quarks and antiquarks, which is based on lattice QCD, is the Born-Oppenheimer approximation [3]. [4,5,6,7,8,9]) as well as tetraquarks with two heavy antiquarks and two light quarks In the latter case, in a first step, potentials of two static antiquarks in the presence of two light quarks are computed using state-of-the-art lattice QCD techniques
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