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

TL;DR

This paper uses a quark model to analyze the proton-omega interaction, explaining experimental correlation functions and supporting the existence of a bound state through energy spectrum, phase shifts, and correlation data.

Contribution

It provides a comprehensive quark-model-based analysis of the $p$-$ Omega$ system, including effective potentials, and explains correlation function features observed experimentally.

Findings

Depletion of correlation functions explained by attractive $J^P=1^+$ component.

Support for the existence of a $p$-$ Omega$ bound state.

Experimental signals of sub-unity correlation function parts.

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.