Production characteristics of light nuclei, hypertritons and $\Omega$-hypernuclei in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV

We extend an analytical nucleon coalescence model with hyperons to study productions of light nuclei, hypertritons and $\Omega$-hypernuclei in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. We derive the formula of the momentum distribution of two bodies coalescing into dibaryon states and that of three bodies coalescing into tribaryon states. We explain the available data of the coalescence factors $B_2$ and $B_3$, the transverse momentum spectra, the averaged transverse momenta, the yield rapidity densities, yield ratios of the deuteron, antihelium-3, antitriton, hypertriton measured by the ALICE collaboration, and give predictions of different $\Omega$-hypernuclei, e.g., $H(p\Omega^-)$, $H(n\Omega^-)$ and $H(pn\Omega^-)$. We find two groups of interesting observables, the averaged transverse momentum ratios of light (hyper-)nuclei to protons (hyperons) and the centrality-dependent yield ratios of theirs. The former group exhibits a reverse-hierarchy of the nucleus size, and the latter is helpful for the judgements of the nucleus production mechanism as well as the nucleus own size.