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

Two-body ⁴He[Formula: see text]-charmonium [Formula: see text] potentials in the single-folding potential (SFP) approach are built by using a first principles HAL QCD low-energy [Formula: see text] and [Formula: see text] interactions. The [Formula: see text] potentials are observed to exhibit an attractive nature across all distances, accompanied by a characteristic long-range tail. It is found that the [Formula: see text] 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 [Formula: see text], no bound or resonance state (with respect to the [Formula: see text] threshold) was found. The [Formula: see text] correlation function in high-energy collisions is examined to explore the [Formula: see text] interaction. The analysis revealed that variations in spin-dependent [Formula: see text] interactions- spin-3/2 [Formula: see text], spin-1/2 [Formula: see text], spin-1/2 [Formula: see text], and the spin-averaged [Formula: see text]-produce noticeable differences in the [Formula: see text] 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 [Formula: see text] system. Furthermore, a comparison has been conducted between two density functions of ⁴He-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 [Formula: see text] binding energies for the two models are nearly indistinguishable, their corresponding correlation functions demonstrate markedly different behaviors. This divergence could yield valuable insights into the nuclear matter distribution function of the alpha particle.