Quantum numbers of excited ${\mathrm{\Xi }}_c^{\mathrm{\prime }}$ and ${\mathrm{\Omega }}_c$ baryons and the $P$-wave ${\mathrm{\Sigma }}_c$ spectrum

Recent precision measurements of excited heavy baryons, combined with systematic theoretical studies, make it possible to resolve the fine structure of their spectra. We calculate the masses and strong-decay properties of the $P$-wave charmed baryons using QCD sum rules and light-cone sum rules within heavy quark effective theory (HQET). Although seven states are allowed in each flavor sector, we find that only four ${\mathrm{\Sigma }}_c$, four ${\mathrm{\Xi }}_c^{\mathrm{\prime }}$, and five ${\mathrm{\Omega }}_c$ states are expected to be experimentally resolvable. The similar mass-splitting patterns of ${\mathrm{\Xi }}_c(2882)$, ${\mathrm{\Xi }}_c(2923)$, ${\mathrm{\Xi }}_c(2939)$, and ${\mathrm{\Xi }}_c(2965)$ and of ${\mathrm{\Omega }}_c(3000)$, ${\mathrm{\Omega }}_c(3050)$, ${\mathrm{\Omega }}_c(3066)$, and ${\mathrm{\Omega }}_c(3090)$, together with our theoretical results, lead to the successive quantum-number assignments $J^P=1\mathrm{/}{2}^{-},3\mathrm{/}{2}^{-},3\mathrm{/}{2}^{-}$, and $5\mathrm{/}{2}^{-}$. We tentatively interpret ${\mathrm{\Omega }}_c(3119)$ as a predominantly $\rho$-mode excitation with $J^P=3\mathrm{/}{2}^{-}$. We also predict the masses, widths, and dominant decay modes of four resolvable $P$-wave ${\mathrm{\Sigma }}_c$ states, which may overlap within the observed ${\mathrm{\Sigma }}_c(2800)$ and ${\mathrm{\Sigma }}_c(2900)$ structures. Precision spectroscopy of the narrow ${\mathrm{\Xi }}_c$ and ${\mathrm{\Omega }}_c$ states thus provides a route to resolving the $P$-wave ${\mathrm{\Sigma }}_c$ spectrum.