The small binding energy of the hypertrition leads to predictions of non-existence of bound hypernuclei for isotriplet three-body systems such as $nn\Lambda$. However, invariant mass spectroscopy at GSI has reported events that may be interpreted as the bound $nn\Lambda$ state. The $nn\Lambda$ state was sought by missing-mass spectroscopy via the $(e,e'K^+)$ reaction at Jefferson Lab's experimental Hall A. The present experiment has higher sensitivity to the $nn\Lambda$-state investigation in terms of better precision by a factor of about three. 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 limits of the production cross-section of the $nn\Lambda$ state were 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 for examining the existence of $nn\Lambda$.
Categories: nucl-ex nucl-th