Eur. Phys. J. A (2024) 60: 3
https://doi.org/10.1140/epja/s10050-023-01219-w

Regular Article - Theoretical Physics

Separation energies of light $\Lambda$ hypernuclei and their theoretical uncertainties

¹ Institut für Kernphysik, Institute for Advanced Simulation and Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany
² Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
³ Tbilisi State University, 0186, Tbilisi, Georgia
⁴ CASA, Forschungszentrum Jülich, 52425, Jülich, Germany

^a h.le@fz-juelich.de

Received: 8 August 2023
Accepted: 12 December 2023
Published online: 6 January 2024

Abstract

Separation energies of light $\Lambda$ hypernuclei ($A\le 5$) and their theoretical uncertainties are investigated. Few-body calculations are performed within the Faddeev-Yakubovsky scheme and the no-core shell model. Thereby, modern and up-to-date nucleon-nucleon, three-nucleon and hyperon-nucleon potentials derived within chiral effective field theory are employed. It is found that the numerical uncertainties of the few-body methods are well under control and an accuracy of around 1 keV for the hypertriton and of better than 20 keV for the separation energies of the ${}_{\Lambda }^4\text{He}$ and ${}_{\Lambda }^5\text{He}$ hypernuclei can be achieved. Variations caused by differences in the nucleon-nucleon interaction are in the order of 10 keV for ${}_{\Lambda }^3\text{H}$ and no more than 110 keV for $A=4,5$$\Lambda$ hypernuclei, when recent high-precision potentials up to fifth order in the chiral expansion are employed. The variations are smaller than the expected contributions from chiral hyperon-nucleon-nucleon forces which arise at the chiral order of state-of-the-art hyperon-nucleon potentials. Estimates for those three-body forces are deduced from a study of the truncation uncertainties in the chiral expansion.