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 $\bar{\Omega}$ 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 produced in baryon-pair production of $\Omega$ with other types of anti-hyperons, such as $\bar{\Xi}$. 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 method to measure the correlation and to demonstrate the general shape of the correlation. We will present the $\Omega$-hadron correlations from simulated $\mathrm{Au}$+$\mathrm{Au}$ collisions at $\sqrt{s_{NN}} = 7.7$ and $14.6 \ \mathrm{GeV}$, and discuss the dependence on collision energy and on the hadronization scheme in these two AMPT versions. These correlations can be used to explore the mechanism of baryon number transport and the effects of baryon number and strangeness conservation in nuclear collisions.