New Ωc0\Omega_c^0 baryons discovered by LHCb as the members of 1P1P and 2S2S states

Inspired by the newly observed $\Omega_c^0$ states at LHCb, we decode their properties by performing an analysis of mass spectrum and decay behavior. Our studies show that the five narrow states, i.e., $\Omega_c(3000)^0$, $\Omega_c(3050)^0$, $\Omega_c(3066)^0$, $\Omega_c(3090)^0$, and $\Omega_c(3119)^0$, could be grouped into the $1P$ states with negative parity. Among them, the $\Omega_c(3000)^0$ and $\Omega_c(3090)^0$ states could be the $J^P=1/2^-$ candidates, while $\Omega_c(3050)^0$ and $\Omega_c(3119)^0$ are suggested as the $J^P=3/2^-$ states. $\Omega_c(3066)^0$ could be regarded as a $J^P=5/2^-$ state. Since the the spin-parity, the electromagnetic transitions, and the possible hadronic decay channels $\Omega_c^{(\ast)}\pi$ have not been measured yet, other explanations are also probable for these narrow $\Omega_c^0$ states. Additionally, we discuss the possibility of the broad structure $\Omega_c(3188)^0$ as a $2S$ state with $J^P=1/2^+$ or $J^P=3/2^+$. In our scheme, $\Omega_c(3119)^0$ cannot be a $2S$ candidate.Comment: 10 pages, 3 figures, 5 tables, typos corrected. Published in Phys. Rev.

Hamilton cycles in almost distance-hereditary graphs

Let $G$ be a graph on $n\geq 3$ vertices. A graph $G$ is almost distance-hereditary if each connected induced subgraph $H$ of $G$ has the property $d_{H}(x,y)\leq d_{G}(x,y)+1$ for any pair of vertices $x,y\in V(H)$. A graph $G$ is called 1-heavy (2-heavy) if at least one (two) of the end vertices of each induced subgraph of $G$ isomorphic to $K_{1,3}$ (a claw) has (have) degree at least $n/2$, and called claw-heavy if each claw of $G$ has a pair of end vertices with degree sum at least $n$. Thus every 2-heavy graph is claw-heavy. In this paper we prove the following two results: (1) Every 2-connected, claw-heavy and almost distance-hereditary graph is Hamiltonian. (2) Every 3-connected, 1-heavy and almost distance-hereditary graph is Hamiltonian. In particular, the first result improves a previous theorem of Feng and Guo. Both results are sharp in some sense.Comment: 14 pages; 1 figure; a new theorem is adde