Quantitative predictions of alpha-charmonium correlation functions in high-energy collisions

Two-body $^{4}\textrm{He}\left(\alpha\right)$-charmonium $\left(c\bar{c}\right)$ potentials in the single-folding potential (SFP) approach are built by using a first principles HAL QCD low-energy $NJ/\psi$ and $N\eta_{c}$ interactions. The $N\textrm{-}c\bar{c}$ potentials are observed to exhibit an attractive nature across all distances, accompanied by a characteristic long-range tail. It is found that the $\alpha\textrm{-}J/\psi$ system appears to be loosely bound with the central binding energy in the range of 0.1-0.6 MeV, while for spin-$1/2$ $\alpha\textrm{-}\eta_{c}$, no bound or resonance state (with respect to the $\alpha \textrm{-} c\bar{c}$ threshold) was found. The $\alpha\textrm{-}c\bar{c}$ correlation function in high-energy collisions is examined to explore the $N\textrm{-}c\bar{c}$ interaction. The analysis revealed that variations in spin-dependent $\alpha\textrm{-}c\bar{c}$ interactions-spin-$3/2$ $\alpha\textrm{-}J/\psi$, spin-$1/2$ $\alpha\textrm{-}J/\psi$, spin-$1/2$ $\alpha\textrm{-}\eta_c$, and the spin-averaged $\alpha\textrm{-}J/\psi$-produce noticeable differences in the $\alpha\textrm{-}c\bar{c}$ correlation function, especially when the source size is around $3$ fm. It is found that different results are produced by the Lednicky-Lyuboshits formula at small source sizes. This indicates that a relatively long-range interaction exists for the $\alpha\textrm{-}c\bar{c}$ system. Furthermore, a comparison has been conducted between two density functions of $^{4}\textrm{He}$ the central depression (CD) and the simple single Gaussian (SG) density-both of which share an identical rms radius of 1.56 fm. Although the $\alpha\textrm{-}J/\psi$ binding energies for the two models are nearly indistinguishable, their corresponding correlation functions demonstrate markedly different behaviors.