Bottomonium resonances with $I = 0$ from lattice QCD correlation functions with static and light quarks

TL;DR

This paper uses lattice QCD correlation functions to study $I=0$ bottomonium resonances and their decay into heavy-light mesons, providing insights into their properties and experimental relevance.

Contribution

It introduces a method to analyze $I=0$ quarkonium resonances using static potentials from lattice QCD, focusing on bottomonium states and their decay channels.

Findings

Computed phase shifts and T-matrix poles for bottomonium decays.

Analyzed static potentials from lattice QCD string breaking studies.

Discussed results in context of $mbda(10860)$ and $mbda(11020)$ experimental states.

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 $\Upsilon (11020)$.