Perspective of $\Lambda$ hyperon production in semi-inclusive DIS with an 11 GeV electron beam at Jefferson Lab

With the planned energy upgrade and the large acceptance CLAS12 detector operated at the high luminosity of $10^{35}$ cm$^{-2}$s$^{-1}$, Jefferson Lab provides unique opportunities to study $\Lambda^0$ hyperon productions in semi-inclusive DIS reactions in the current fragmentation regime ($x_F>0$, $z>0.5$). Based on the LUND model and the recent HERMES data, we carried out numerical estimations of the following physics observables: 1. lepton to $\Lambda$ longitudinal spin transfer, 2. beam-target double-spin asymmetries, 3. nucleon to $\Lambda$ spin transfer, 4. Induced $\Lambda$ polarization on an unpolarized target, 5. transverse $\Lambda$ polarization on a transversely polarized target. The projected statistical accuracies will be compared with existing theory models and recent data from the COMPASS and the HERMES collaborations.