The origin of excited states of the $Λ$ baryon at the SU(3) point from Lattice QCD

Abstract

In this work we determine the finite-volume lattice QCD spectrum at the flavor symmetric $\mathrm{SU}(3)$ point in the meson-baryon singlet and octet irreducible representations. We construct the appropriate interpolation operators and perform the calculation on ensembles in quite large volume ($L=48$). We find three below-threshold energy levels, with the singlet having lower energy and the two octets being non-degenerate at one sigma, which for these large volumes ($M_π L\approx 14.5$) strongly suggests a bound state close to that energy at each of the irreducible representations. We confront this finite-volume spectrum with the prediction from UCHPT through the Lüscher method finding qualitative agreement. Finally we perform a re-fit of UCHPT free parameters to the available (experimental and lattice) data including the energy levels calculated in this work. This allows us to follow the pole trajectories to the physical point, identifying the $Λ(1405)$ as a lower octet, and $Λ(1380)$ as a singlet bound state in the $\mathrm{SU(3)}$ limit. Furthermore, $Λ(1670)$ is identified on a qualitative level as the heavier octet bound state and its relation to three-body final states is discussed.