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

TL;DR

This paper uses lattice QCD to analyze the coupled $c ext{Sigma}-ar{K}N$ scattering and the $b1405$ resonance, revealing a virtual bound state and a resonance pole near thresholds.

Contribution

It provides a first-principles lattice QCD calculation of the coupled-channel scattering amplitudes relevant to the $b1405$ resonance, using multiple parametrizations and a single gauge ensemble.

Findings

Identification of a virtual bound state below the $c ext{Sigma}$ threshold.

Detection of a resonance pole just below the $ar{K}N$ threshold.

Use of multiple parametrizations to extract scattering amplitudes.

Abstract

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