Resonances in coupled $\pi K, \eta K$ scattering from lattice QCD

TL;DR

This study uses lattice QCD to analyze coupled $$ and $$ scattering, revealing resonances and virtual states relevant to meson interactions and resonance structures.

Contribution

It provides the first lattice QCD determination of coupled-channel $$ and $$ scattering amplitudes, identifying multiple resonances and virtual states.

Findings

Identification of a broad scalar resonance in $$ scattering.

Evidence for a $$-like bound state near threshold.

Observation of a narrow $2^+$ resonance.

Abstract

Coupled-channel $\pi K$ and $\eta K$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $q\bar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_\pi=391\,\mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $\pi K$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $\pi K$ and weakly to $\eta K$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $\kappa$ resonance. A bound state with $J^P=1^-$ is found very close to the $\pi K$ threshold energy, whose coupling to the $\pi K$ channel is compatible with that of the experimental $K^\star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $\pi K$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.