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

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 $N_{\mathrm{f}}=2+1$ 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 $\pi \Sigma$ threshold and a resonance pole just below the $\bar{K}N$ threshold.

18 pages, 11 figures, 14 tables. Final version accepted for publication in PRD with post-publication corrections

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• Two-pole nature of the $\Lambda (1405)$ from lattice QCD
• Structure of the $\mathbf{\Lambda }(1670)$ resonance
• Compositeness of hadrons, nuclei, and atomic systems
• Pole trajectories of the $\Lambda (1405)$ helps establish its dynamical nature
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• The odd-parity strange baryons $\Sigma ({\frac{1}{2}}^{-})$ below 1.8 GeV with Hamiltonian effective field theory
• Odd-Parity Nucleon Electromagnetic Transitions in Lattice QCD
• Perturbative application of next-to-leading order pionless EFT for $A\le 3$ nuclei in a finite volume
• Position-space sampling for local multiquark operators in lattice QCD using distillation and the importance of tetraquark operators for $T_{cc}(3875{)}^{+}$
• Chirally motivated $\pi \Sigma$-$\bar{K}N$ model in a finite volume
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram
• Higher order quantization conditions for two-body scattering with spin