Quantum Numbers of $Ω_c$ States and Other Charmed Baryons

Abstract

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 $Ω_c$ states, we have identified $Ω_c(3090)$ and $Ω_c(3119)$ with radially excited $\frac12^+(2S)$ and $\frac32^+(2S)$ states, respectively, and $Ω_c(3000)$ with $\frac12^-(1P)$ and $S=\frac32$. The two states $Ω_c(3050)$ and $Ω_c(3066)$ form a $P$-wave $(\frac32^-,\frac52^-)$ doublet. (ii) The widths of $Ω_c(3066)$ and $Ξ'_c(2930)$ are calculable within the framework of heavy hadron chiral perturbation theory. (iii) Since the width of $Ω_{c0}(\frac12^-)$ is of order 410 MeV, not all observed narrow $Ω_c$ baryons can be identified with $1P$ states. (iv) For the antitriplet $Λ_c$ and $Ξ_c$ 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 $Λ_c(2940)$ does not fit if its quantum numbers are $\frac32^-$ as found by LHCb. We suggest that $Λ_c(2940)^+$ is most likely the $\frac12^-(2P)$ state. (v) The charmed baryon $Σ_c(2800)$ 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 $Ξ'_c$ states, we find a missing state. It should have quantum numbers $\frac52^-$ with a mass around 2920~MeV.

21 pages, 7 figures. Sec. II.A is substantially revised. Quantum number assignment to Omega_c(3050) and Omega_c(3066) is modified. Two more figures for the Regge trajectories in the (n_r, M^2) plane