A Practical Partial-Wave Method for Identifying Unstable Light Nucleus Resonances in Heavy-Ion Collisions

Abstract: The production of light nuclei in relativistic heavy-ion collisions provides valuable insights into the dynamics of the hot and dense matter created in these extreme environments. While stable light nuclei have been extensively studied, unstable light nuclei being short-lived resonance states remain largely unexplored and offer unique opportunities to probe final-state interactions and the freeze-out conditions. In this paper, we propose a partial-wave method, based on the Lednický--Lyuboshitz framework, to extract resonance signals of unstable light nuclei from two-particle correlation functions measured in heavy-ion collisions. By extending the LL model to higher order partial waves and directly incorporating experimental phase-shift data from low-energy nuclear scattering, our approach avoids the need for model-dependent potential parametrizations and enables a clean decomposition of the resonant partial wave from the non-resonant background. As a demonstration, we apply the method to the $p$-$<sup>3$He and $p$-$<sup>4$He systems, corresponding to the $<sup>4$Li and $<sup>5$Li ground-state resonances. Numerical results show that the resonance-induced correlation excess can be effectively isolated, with a peak in the correlation function appearing at $k \approx 72$ MeV/$c$ for $<sup>4$Li and $k \approx 50$ MeV/$c$ for $<sup>5$Li, consistent with the known resonance parameters. The extracted transverse momentum spectra and rapidity distributions are presented using the measured proton and light-nuclei spectra from STAR at $\sqrt{s_{NN}} = 3$ GeV. The proposed method provides a practical tool for the experimental study of unstable light nuclei in relativistic heavy-ion collisions and can be extended to a broader range of resonance states.