Productions of ${}_{\mathrm{\Lambda }}^3$H, ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$He in different coalescence channels in Au-Au collisions at $\sqrt{s_{NN}}=3$ GeV

We study the productions of $\mathrm{\Lambda }$-hypernuclei ${}_{\mathrm{\Lambda }}^3$H, ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$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$+\mathrm{\Lambda }$ coalescence but also nucleus+nucleon($\mathrm{\Lambda }$) coalescence. We present contributions from different coalescence channels for ${}_{\mathrm{\Lambda }}^3$H, ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$He in their productions. We predict the production asymmetry between ${}_{\mathrm{\Lambda }}^4$H and ${}_{\mathrm{\Lambda }}^4$He, characterized by yield ratios ${}_{\mathrm{\Lambda }}^4\text{He}{\mathrm{/}}_{\mathrm{\Lambda }}^4\text{H}$ and ${(}_{\mathrm{\Lambda }}^4\text{H}{-}_{\mathrm{\Lambda }}^4\text{He})\mathrm{/}{(}_{\mathrm{\Lambda }}^4\text{H}{+}_{\mathrm{\Lambda }}^4\text{He})$, which can shed light on the existence constraints of the possible neutron-$\mathrm{\Lambda }$ bound states ${}_{\mathrm{\Lambda }}^{2}n(n\mathrm{\Lambda })$ and ${}_{\mathrm{\Lambda }}^{3}n(nn\mathrm{\Lambda })$.