Determining the Unknown $\Lambda -n$ Interaction by Investigating the $\Lambda nn$ Resonance

The newly approved Jlab experiment E12-17-003 is to search and measure the $\Lambda$ binding energy $(B_{\Lambda})$ and natural width $(\Gamma_{\Lambda})$ of a possible $\Lambda nn$ three-body resonance, using the $^{3}H(e,e',K^{+})\Lambda nn$ reaction with the high quality CEBAF electron beam and the Hall A high resolution spectrometers. This resonance, if exists as indicated by the result of HypHI experiment [1] and predicted by theory [2], should be a pure isospin T = 1 stae. With the highest possible precision achievable by electro-production from the jlab experiment, the measured $B_{\Lambda}$ and $\Gamma_{\Lambda}$ can be used to investigate and determine the unknown $\Lambda n$ interaction, experimentally for the first time, relative to $\Lambda p$ interaction fitted from limited $\Lambda p$ scattering data. The measurement may provide important clues to the long stand puzzle of charge-symmetry-breaking(CSB) in $\Lambda N$ interactions and it may impact on your understanding on hypernuclei and EOS of neutron stars. \\ \setlength{\parindent}{0cm} [1] C. Rappold et al.,Phys.Rev. C88, 041001(R) (2013) [2] Iraj R. Afnan and Benjamin F. Gibson, Phys. Rev. C92, 054608 (2015)