Production of the superheavy baryon Λccˉ∗(4209)\Lambda _{c\bar{c}}^{\ast}(4209) in kaon-induced reaction

The production of superheavy $\Lambda _{c\bar{c}}^{\ast }(4209)$ baryon in the $K^{-}p\rightarrow \eta _{c}\Lambda$ process via $s$-channel is investigated with an effective Lagrangian approach and the isobar model. Moreover, the $t$-channel with $K^{\ast }$ and $u$-channel with nucleon exchange are also considered, which are regarded as the background for the $\Lambda _{c\bar{c}}^{\ast }(4209)$ production in the $K^{-}p\rightarrow \eta_{c}\Lambda$ reaction. The numerical results indicate it is feasible to searching for the superheavy $\Lambda _{c\bar{c}}^{\ast }(4209)$ via $K^{-}p$ scattering. These theoretical results not only provide valuable informations to future experimental exploration of $\Lambda _{c\bar{c}}^{\ast }(4209)$ resonance but enable us to have a better understanding of the exotic baryons.Comment: 6 page

Quantitative Volume Space Form Rigidity Under Lower Ricci Curvature Bound

Let $M$ be a compact $n$-manifold of $\operatorname{Ric}_M\ge (n-1)H$ ($H$ is a constant). We are concerned with the following space form rigidity: $M$ is isometric to a space form of constant curvature $H$ under either of the following conditions: (i) There is $\rho>0$ such that for any $x\in M$, the open $\rho$-ball at $x^*$ in the (local) Riemannian universal covering space, $(U^*_\rho,x^*)\to (B_\rho(x),x)$, has the maximal volume i.e., the volume of a $\rho$-ball in the simply connected $n$-space form of curvature $H$. (ii) For $H=-1$, the volume entropy of $M$ is maximal i.e. $n-1$ ([LW1]). The main results of this paper are quantitative space form rigidity i.e., statements that $M$ is diffeomorphic and close in the Gromov-Hausdorff topology to a space form of constant curvature $H$, if $M$ almost satisfies, under some additional condition, the above maximal volume condition. For $H=1$, the quantitative spherical space form rigidity improves and generalizes the diffeomorphic sphere theorem in [CC2].Comment: The only change from the early version is an improvement on Theorem A: we replace the non-collapsing condition on $M$ by on $\tilde M$ (the Riemannian universal cover), and the corresponding modification is adding "subsection c" in Section