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

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• Hypernuclei & mesic nuclei
• Particle & resonance production
• Relativistic heavy-ion collisions