Bottomonium resonances with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math> from lattice QCD correlation functions with static and light quarks
Pedro Bicudo, Marco Cardoso, Nuno Cardoso, Marc Wagner
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 ${L}_{\overline{Q}Q}=0$ of the $\overline{b}b$ pair corresponding to ${J}^{PC}={0}^{\ensuremath{-}+}$ and ${J}^{PC}={1}^{\ensuremath{-}\ensuremath{-}}$. We use static potentials from an existing lattice QCD string breaking study and compute phase shifts and $\mathrm{T}$ 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 $\mathrm{\ensuremath{\Upsilon}}(10860)$ and $\mathrm{\ensuremath{\Upsilon}}(11020)$.