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 $q\overline{q}$ 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 nonresonant phase shifts spanning the whole elastic scattering region are obtained.

• Received 14 November 2014

DOI:https://doi.org/10.1103/PhysRevD.91.054008