Study of Baryon Number Transport Dynamics and Strangeness Conservation Effects Using $\Omega$-hadron Correlations

In nuclear collisions at RHIC energies, an excess of $\Omega$ hyperons over $\overline{\Omega}$ is observed, indicating that $\Omega$ carries a net baryon number despite $s$ and $\bar{s}$ quarks being produced in pairs. The baryon number in $\Omega$ could have been transported from the incident nuclei and/or acquired and balanced in baryon pair productions associated with other types of anti-hyperons, such as $\overline{\Xi}$. To investigate these two scenarios, we propose to measure correlations between $\Omega$ and $K$, as well as between $\Omega$ and anti-hyperons. We will use two versions, the default and string-melting, of a multiphase transport (AMPT) model to illustrate the correlation method. We will present the $\Omega$-hadron correlations from simulated Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ and 14.6 GeV, and discuss the dependence on collision energy and on the hadronization scheme in these two AMPT versions. These correlations from the AMPT model provide a baseline for experimental exploration of the dynamics of baryon number transport and the effects of baryon number and strangeness conservation in nuclear collisions.