Lattice QCD study of $\pi\Sigma\unicode{x2013}\bar{K}N$ scattering and the $\Lambda(1405)$ resonance

Bulava, John; Morningstar, Colin; Hanlon, Andrew D.; Walker-Loud, André; Cid-Mora, Bárbara; Skinner, Sarah; Mohler, Daniel; Hörz, Ben; Romero-López, Fernando; Moscoso, Joseph; Nicholson, Amy

Preprint

PUBDB-2023-04593

Lattice QCD study of $\pi\Sigma\unicode{x2013}\bar{K}N$ scattering and the $\Lambda(1405)$ resonance

Bulava, J.DESY* ; Cid-Mora, B. ; Hanlon, A. D. ; Hörz, B. ; Mohler, D. ; Morningstar, C. ; Moscoso, J. ; Nicholson, A. ; Romero-López, F. ; Skinner, S. ; Walker-Loud, A.

2023

[10.3204/PUBDB-2023-04593]

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Report No.: MIT-CTP/5580; arXiv:2307.13471

Abstract: A lattice QCD computation of the coupled channel $\pi\Sigma\unicode{x2013}\bar{K}N$ 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.

Keyword(s): resonance, pole ; quark, flavor ; lattice field theory ; Lambda(1405) ; scattering amplitude ; scattering ; baryon ; correlation ; parametrization ; gauge field theory ; meson baryon ; bound state ; coupled channel ; finite size