The cross-section measurement for the $^3{\rm H}(e,e'K^+)nn\Lambda$ reaction.

The small binding energy of hypertrition leads to predictions of non-existence of bound hypernuclei for the isotriplet three-body system such as $nn\Lambda$. However, invariant mass spectroscopy at GSI reported events that may be interpreted as the bound $nn\Lambda$ state. The $nn\Lambda$ state was searched by missing-mass spectroscopy via the $(e,e'K^+)$ reaction at the Jefferson Lab's experimental Hall A. The present experiment has higher sensitivity to the $nn\Lambda$-state investigation in terms of the better precision by a factor of about three than the previous invariant mass spectroscopy. The analysis shown in this article focuses on the derivation of the reaction-cross section for the $^3{\rm{H}}(\gamma^{*},K^+)\textrm{X}$ reaction. Events that were detected in an acceptance, where a Monte Carlo simulation could reproduce the data well ($|\delta p/p| < 4\%$), were analyzed to minimize the systematic uncertainty. No significant structures were observed with the acceptance cuts, and the upper limit of the reaction-cross section of $nn\Lambda$ state was obtained to be $21$ and $31~\rm{nb/sr}$ at the $90\%$-confidence level when theoretical predictions of $(-B_{\Lambda}, \Gamma) = (0.25,0.8)$ and $(0.55, 4.7)$ MeV, respectively, were assumed. The cross-section result provides valuable information to examine the existence of $nn\Lambda$.