Quantum Numbers of ${\Omega }_c$ 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 ${\Omega }_c$ states, we have identified ${\Omega }_c(3090)$ and ${\Omega }_c(3119)$ with radially excited ${\frac{1}{2}}^{+}(2S)$ and ${\frac{3}{2}}^{+}(2S)$ states, respectively, and ${\Omega }_c(3000)$ with ${\frac{1}{2}}^{-}(1P)$ and $S=\frac{3}{2}$. The two states ${\Omega }_c(3050)$ and ${\Omega }_c(3066)$ form a $P$-wave $({\frac{3}{2}}^{-},{\frac{5}{2}}^{-})$ doublet. (ii) The widths of ${\Omega }_c(3066)$ and ${\Xi }_c^{\prime }(2930)$ are calculable within the framework of heavy hadron chiral perturbation theory. (iii) Since the width of ${\Omega }_{c0}({\frac{1}{2}}^{-})$ 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 ${\frac{1}{2}}^{-}$ and ${\frac{3}{2}}^{-}$ 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 ${\frac{3}{2}}^{-}$ as found by LHCb. We suggest that ${\Lambda }_c(2940{)}^{+}$ is most likely the ${\frac{1}{2}}^{-}(2P)$ state. (v) The charmed baryon ${\Sigma }_c(2800)$ cannot be a ${\frac{1}{2}}^{-}$ state; otherwise, its width will be over 400~MeV, too large compared to the measured one. (vi) In the study of Regge trajectories of ${\Xi }_c^{\prime }$ states, we find a missing state. It should have quantum numbers ${\frac{5}{2}}^{-}$ with a mass around 2920~MeV.

Comments: 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