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