Lattice QCD study of $\pi \mathrm{\Sigma }-\bar{K}N$ scattering and the $\mathrm{\Lambda }(1405)$ resonance

A lattice QCD computation of the coupled channel $\pi \mathrm{\Sigma }-\bar{K}N$ scattering amplitudes in the $\mathrm{\Lambda }(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\mathrm{f}}=2+1$ dynamical quark flavors and $m_{\pi }\approx 200$ MeV and $m_K\approx 487$ 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 $\pi \mathrm{\Sigma }$ threshold and a resonance pole just below the $\bar{K}N$ threshold.