Production correlation of light (hyper-)nuclei in Au-Au collisions from the RHIC Beam Energy Scan

Based on nucleons ($p$, $n$) and hyperons ($\mathrm{\Lambda }$, ${\mathrm{\Omega }}^{-}$) formed at kinetic freeze-out from a quark combination model, we systematically study the production of light nuclei and hyper-nuclei in the hadronic coalescence picture. We present the analytical formula of the nucleus momentum distribution of two-body coalescence and that of three-body coalescence. We explain the experimental data of the transverse momentum spectra of deuteron ($d$), triton ($t$), helium-3 (${}^3$He) and hypertriton (${}_{\mathrm{\Lambda }}^3$H) measured in Au-Au collisions from the RHIC Beam Energy Scan I and II, and also provide the corresponding predictions of different $\mathrm{\Omega }-$hypernuclei $H(p{\mathrm{\Omega }}^{-})$, $H(n{\mathrm{\Omega }}^{-})$ and $H(pn{\mathrm{\Omega }}^{-})$. We further study the production correlations of different species of light (hyper-)nuclei and discuss their interesting behaviors as a function of collision energy.