Resonances in coupled $πK, ηK$ scattering from lattice QCD

Abstract

Coupled-channel $πK$ and $ηK$ 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 ${m_π=391\,\mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $πK$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $πK$ and weakly to $ηK$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $κ$ resonance. A bound state with $J^P=1^-$ is found very close to the $πK$ threshold energy, whose coupling to the $πK$ 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 $πK$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.

32 pages, 27 figures - replaced to better match version appearing in PRD. Previously incorrect JLab preprint number also corrected