We study the productions of $\Lambda$-hypernuclei $^3_{ \Lambda}$H, $^4_{ \Lambda}$H and $^4_{ \Lambda}$He in the coalescence mechanism in Au-Au collisions at $\sqrt{ s_{ NN}}=3$ GeV. Considering the abundance and great importance of baryons and light (hyper-)nuclei on the collision dynamics, we include not only nucleon$+\Lambda$ coalescence but also nucleus+nucleon($\Lambda$) coalescence. We present contributions from different coalescence channels for $^3_{ \Lambda}$H, $^4_{ \Lambda}$H and $^4_{ \Lambda}$He in their productions. We predict the production asymmetry between $^4_{ \Lambda}$H and $^4_{ \Lambda}$He, characterized by yield ratios $^4_{ \Lambda}\text{ He}/^4_{ \Lambda}\text{ H}$ and $(^4_{ \Lambda}\text{ H}-^4_{ \Lambda}\text{ He})/(^4_{ \Lambda}\text{ H}+^4_{ \Lambda}\text{ He})$, which can shed light on the existence constraints of the possible neutron-$\Lambda$ bound states $^2_{ \Lambda}n~(n\Lambda)$ and $^3_{ \Lambda}n~(nn\Lambda)$.
Categories: nucl-th hep-ex hep-ph nucl-ex