Lattice QCD study of $πΣ-\bar{K}N$ scattering and the $Λ(1405)$ resonance

A lattice QCD computation of the coupled channel $πΣ-\bar{K}N$ scattering amplitudes in the $Λ(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_π \approx 200$ MeV and $m_K\approx487$ MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering $K$-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the $πΣ$ threshold and a resonance pole just below the $\bar{K}N$ threshold.