Measurement of 3,4He( K − , π 0 ) Λ 3 , 4 H reaction cross section and evaluation of hypertriton Λ binding energy

Light $s$-shell hypernuclei ($^{3,4}_Λ\text{H}$) and their ground-state properties are crucial benchmarks in hypernuclear physics. In particular, comparing the production cross sections of $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$ provides insights into the $ΛN$ interaction in different isospin configurations, which can help address recent discrepancies in the reported $Λ$ binding energy of hypertriton. We present the first measurement of the production cross sections for $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$ using the in-flight $(K^-, π^0)$ 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$^{\circ}$ to 20$^{\circ}$, are measured to be $15.0~\pm~2.6~(\text{stat.})~^{+2.4}_{-2.8}~(\text{syst.})~μ\text{b} $ and $49.9~\pm~2.1~(\text{stat.})~^{+7.8}_{-8.0}~(\text{syst.})~μ\text{b}$ for the ground-state of $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$, respectively. Using the ratio of these cross sections and comparing it with theoretical calculations, we evaluate the $Λ$ binding energy of hypertriton, yielding a value consistent with the picture of a loosely bound system.