Measurement of 3,4He(K⁻, π⁰)3,4_ΛH reaction cross section and evaluation of hypertriton binding energy

Light s-shell hypernuclei (3,4_ΛH) and their ground-state properties are crucial benchmarks in hypernuclear physics. In particular, comparing the production cross sections of ³_ΛH and ⁴_ΛH provides insights into the $ΛN$ interaction in different isospin configurations, which can help address recent discrepancies in the reported binding energy of hypertriton. We present the first measurement of the production cross sections for ³_ΛH and ⁴_ΛH using the in-flight (K⁻, π⁰) reaction at a beam momentum of 1.0 GeV/c with an identical experimental setup. The production cross sections in the laboratory frame, for the angular range from 0∘ to 20∘, are measured to be: 15.0~±~2.6~(stat.)~+2.4-2.8~(syst.)~μb and 50.7~±~2.1~(stat.)~+7.8-8.3~(syst.)~μb, respectively. Using the ratio of the cross sections and comparing the ratio with theoretical calculations, we evaluate the hypertriton binding energy to be 0.061\ +0.028-0.022\ (stat.)\ +0.024-0.021\ (syst.)\ MeV.