Investigating the $p$-$\Omega$ Interaction and Correlation Functions

Abstract

Motivated by experimental measurements, we investigate the $p$-$\Omega$ correlation functions and interactions on the basis of a quark model. By solving the inverse scattering problem with channel coupling, we renormalize the coupling to other channels into an effective single-channel $p$-$\Omega$ potentials. The effects of Coulomb interaction and spin-averaging are also discussed. According to our results, the depletion of the $p$-$\Omega$ correlation functions, which is attributed to the $J^P = 2^+$ bound state not observed in the ALICE Collaboration's measurements [Nature \textbf{588}, 232 (2020)], can be explained by the contribution of the attractive $J^P = 1^+$ component in spin-averaging. So far, we have provided a consistent description of the $p$-$\Omega$ system from the perspective of the quark model, including the energy spectrum, scattering phase shifts, and correlation functions. The existence of the $p$-$\Omega$ bound state has been supported by all three aspects. Additionally, a sign of the $p$-$\Omega$ correlation function's subtle sub-unity part can be seen in experimental measurements, which warrants more precise verification in the future.