Quantum Numbers of $\Omega_c$ States and Other Charmed Baryons

Possible spin-parity quantum numbers for excited charmed baryon resonances are discussed in this work. Our main results are: (i) Among the five newly observed $\Omega_c$ states, we have identified $\Omega_c(3090)$ and $\Omega_c(3119)$ with radially excited $\frac12^+(2S)$ and $\frac32^+(2S)$ states, respectively, and $\Omega_c(3000)$ with $\frac12^-(1P)$ and $S=\frac32$. The two states $\Omega_c(3050)$ and $\Omega_c(3066)$ form a $P$-wave $(\frac32^-,\frac52^-)$ doublet. (ii) The widths of $\Omega_c(3066)$ and $\Xi'_c(2930)$ are calculable within the framework of heavy hadron chiral perturbation theory. (iii) Since the width of $\Omega_{c0}(\frac12^-)$ is of order 410 MeV, not all observed narrow $\Omega_c$ baryons can be identified with $1P$ states. (iv) For the antitriplet $\Lambda_c$ and $\Xi_c$ states, their Regge trajectories for the orbital excitations of $\frac12^-$ and $\frac32^-$ are parallel to each other. Based on this nice property of parallelism, we see that the highest state $\Lambda_c(2940)$ does not fit if its quantum numbers are $\frac32^-$ as found by LHCb. We suggest that $\Lambda_c(2940)^+$ is most likely the $\frac12^-(2P)$ state. (v) The charmed baryon $\Sigma_c(2800)$ cannot be a $\frac12^-$ state; otherwise, its width will be over 400~MeV, too large compared to the measured one. (vi) In the study of Regge trajectories of $\Xi'_c$ states, we find a missing state. It should have quantum numbers $\frac52^-$ with a mass around 2920~MeV.