Two-pole nature of the $\Lambda (1405)$ from lattice QCD

Abstract

This letter presents the first lattice QCD computation of the coupled channel $\pi \Sigma -\bar{K}N$ scattering amplitudes at energies near $1405\mathrm{MeV}$. These amplitudes contain the resonance $\Lambda (1405)$ with strangeness $S=-1$ and isospin, spin, and parity quantum numbers $I(J^P)=0(1/2^{-})$. However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to $m_{\pi }\approx 200$ MeV and $m_K\approx 487$ MeV, this study finds the amplitudes exhibit a virtual bound state below the $\pi \Sigma$ threshold in addition to the established resonance pole just below the $\bar{K}N$ threshold. Several parametrizations of the two-channel $K$-matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by $SU(3)$ chiral symmetry and unitarity.

Comments: 7 pages, 4 figures, and 1 table. Includes various corrections made during the last stages before publication