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

## TL;DR

This paper analyzes the quantum numbers of excited charmed baryons, especially $ ext{Omega}_c$ states, assigning specific spin-parity states, calculating widths, and discussing their placement on Regge trajectories to clarify their identities.

## Contribution

The work provides a detailed quantum number assignment for newly observed $ ext{Omega}_c$ states and explores their widths and Regge trajectories, offering insights into their structure and classification.

## Key findings

- $ ext{Omega}_c(3090)$ and $ ext{Omega}_c(3119)$ are identified as radially excited states.
- Widths of $ ext{Omega}_c(3066)$ and $ ext{Xi}'_c(2930)$ are calculated within heavy hadron chiral perturbation theory.
- $ ext{Lambda}_c(2940)$ is most likely a $rac12^-(2P)$ state, not $rac32^-$ as previously suggested.

## 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 $\frac12^+(2S)$ 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.