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

Abstract

AbstractSeparation energies of light $$\varLambda $$ Λ hypernuclei ($$A\le 5$$ A ≤ 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 $$^{\,4}_{\varLambda }\textrm{He}$$ Λ 4 He and $$^{\,5}_{\varLambda }\textrm{He}$$ Λ 5 He hypernuclei can be achieved. Variations caused by differences in the nucleon-nucleon interaction are in the order of 10 keV for $$^{\,3}_{\varLambda }\textrm{H}$$ Λ 3 H and no more than 110 keV for $$A=4,\,5$$ A = 4 , 5 $$\varLambda $$ Λ 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.