Separation energies of light Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hypernuclei and their theoretical uncertainties

Abstract

Separation energies of light Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hypernuclei (A≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\\le 5$$\\end{document}) 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 Λ4He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,4}_{\\varLambda }\ extrm{He}$$\\end{document} and Λ5He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,5}_{\\varLambda }\ extrm{He}$$\\end{document} hypernuclei can be achieved. Variations caused by differences in the nucleon-nucleon interaction are in the order of 10 keV for Λ3H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,3}_{\\varLambda }\ extrm{H}$$\\end{document} and no more than 110 keV for A=4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=4,\\,5$$\\end{document}Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} 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.