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In this article, we present a complete classification of the negative parity$\Xi'_{c/b}$ and $\Xi_{c/b}$ $P$-wave states: 7 belonging to the $SU(3)$ flavorsextet and 7 to the flavor anti-triplet, the calculation of the $\Xi'_{c/b}$and $\Xi_{c/b}$ strong partial decay widths into $^2\Sigma_c \bar{K}$,$^2\Xi_c^{'} \pi$, $^2\Sigma_c \bar{K}$, $^4\Xi_c^{'} \pi$, $\Lambda_c^{'}\bar{K}$, $\Xi_c^{} \pi$ and $\Xi_c^{} \eta$ channels both within theElementary Emission Model (EEM) and the $^3P_0$ model, and the calculation ofthe electromagnetic decay widths for $\Xi'_{c/b}$ and $\Xi_{c/b}$ radiativedecays. By means of the equal-spacing mass rule and by the analysis of thestrong partial decay widths, we suggest possible assignments for the new LHCb$\Xi_{c}(2923)$, $\Xi_{c}(2939)$, and $\Xi_{c}(2965)$ states, as well as forthe $\Xi_{c}$'s previously reported by Belle and BaBar. Our results can betested by future experiments, at LHCb and Belle, disentangling the remainingmissing piece of information, {\it i.e.} the quantum numbers. Finally, acomparison is made between a three-quark and a quark-diquark description of$\Xi_c$ states. Very recently the LHCb collaboration reported the observationof two new $\Xi_b$ states, namely $\Xi_b(6327)^{0}$ and $\Xi_b(6333)$, in$\Lambda_b^0 K^{-} \pi^{+}$ channel with a statistical significance larger thannine standard deviations. The experimental masses and widths of these twostates are consistent with our mass and width predictions for the doublet ofD-wave excitations of the $\Xi_b$ system with$J^{P}_{\Xi_b(6327)^{0}}=\frac{3}{2}^{+}$ and$J^{P}_{\Xi_b(6333)^{0}}=\frac{5}{2}^{+}$.

Masses and decay widths of $\Xi_{c/b}$ and $\Xi^\prime_{c/b}$ baryons