Measurement of ${}^{3,4}$He($K^{-},\ddot{I}{€}^0$)${}_{\hat{I}}^{3,4}›$H reaction cross section and evaluation of hypertriton $\hat{I}›$ binding energy

Abstract

Light $s$-shell hypernuclei (${}_{\hat{I}}^{3,4}›\text{H}$) and their ground-state properties are crucial benchmarks in hypernuclear physics. In particular, comparing the production cross sections of ${}_{\hat{I}}^3›\text{H}$ and ${}_{\hat{I}}^4›\text{H}$ provides insights into the $\hat{I}›N$ interaction in different isospin configurations, which can help address recent discrepancies in the reported $\hat{I}›$ binding energy of hypertriton. We present the first measurement of the production cross sections for ${}_{\hat{I}}^3›\text{H}$ and ${}_{\hat{I}}^4›\text{H}$ using the in-flight $(K^{-},\ddot{I}{€}^0)$ 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 $15.0\pm 2.6(\text{stat.}){}_{-2.8}^{+2.4}(\text{syst.})\hat{I}¼\text{b}$ and $49.9\pm 2.1(\text{stat.}){}_{-8.0}^{+7.8}(\text{syst.})\hat{I}¼\text{b}$ for the ground-state of ${}_{\hat{I}}^3›\text{H}$ and ${}_{\hat{I}}^4›\text{H}$, respectively. Using the ratio of these cross sections and comparing it with theoretical calculations, we evaluate the $\hat{I}›$ binding energy of hypertriton, yielding a value consistent with the picture of a loosely bound system.