Quantum numbers of excited $\Xi_c^\prime$ and $\Omega_c$ baryons and the $P$-wave $\Sigma_c$ spectrum

Abstract

Heavy quark effective theory (HQET) permits seven $P$-wave states in each of the $\Sigma_c$, $\Xi_c^\prime$, and $\Omega_c$ flavor-sextet sectors, yet the experimentally visible spectra differ strikingly among the three sectors. We show that strong decays, kinematic thresholds, and configuration mixing act as a dynamical filter between the underlying multiplet structure and the observed resonance spectrum. Using QCD sum rules for the masses and light-cone sum rules for the strong decays, we find that only four $\Sigma_c$, four $\Xi_c^\prime$, and five $\Omega_c$ states are sufficiently narrow to contribute to experimentally identifiable resonance structures. The four narrow $\Xi_c$ states, $\Xi_c(2882)$, $\Xi_c(2923)$, $\Xi_c(2939)$, and $\Xi_c(2965)$, and the four narrow $\Omega_c$ states, $\Omega_c(3000)$, $\Omega_c(3050)$, $\Omega_c(3066)$, and $\Omega_c(3090)$, exhibit similar mass-splitting patterns and provide spectroscopic anchors for a common $\lambda$-mode multiplet structure, supporting the successive assignments $J^P=1/2^-,3/2^-,3/2^-$, and $5/2^-$. We tentatively interpret $\Omega_c(3119)$ as a predominantly $\rho$-mode state with $J^P=3/2^-$. With this multiplet structure constrained by the $\Xi_c$ and $\Omega_c$ spectra, we predict four relatively resolvable $P$-wave $\Sigma_c$ states that may overlap within the observed $\Sigma_c(2800)$ and $\Sigma_c(2900)$ structures, providing concrete targets for future amplitude analyses.