Mass spectrum and magnetic moments of singly-charmed baryons: a quark-diquark model analysis of $\Omega_{c}(3185)^0$ and $\Omega_c(3327)^0$

Research on singly-heavy baryons, especially those with a charm quark, offers a distinct perspective on the nonperturbative behavior of Quantum Chromodynamics (QCD). In this work, we investigate the recently observed $\Omega_{c}(3185)^{0}$ and $\Omega_{c}(3327)^{0}$ are singly-charmed baryons within the framework of the quark-diquark model. By employing a nonrelativistic method with a Cornell-like potential, we systematically determine magnetic moments and mass spectra. Our analysis reveals that the $\Omega_{c}(3185)^{0}$ can be effectively described as a $2S$ state with quantum numbers $J^{P}=\frac{1}{2}^{+}$ or $\frac{3}{2}^{+}$, or alternatively as a $1P$ state with $J^{P}=\frac{1}{2}^{-}$ or $\frac{3}{2}^{-}$, depending on the diquark configuration. Similarly, the $\Omega_{c}(3327)^{0}$ is consistent with a $2S$ configuration. We also investigate through magnetic moments, emphasizing the critical role of diquark correlations in shaping the electromagnetic properties of these states. Our results not only validate existing theoretical models but also offer new insights into the nature of singly-heavy baryons, setting the stage for future experimental and theoretical investigations in heavy baryon spectroscopy. This paper emphasizes the importance of diquark configurations in elucidating the mass spectrum and electromagnetic characteristics of singly-charmed baryons, aiding the overarching endeavor to decipher the intricacies of QCD.