Towards two-body strong decay behavior of higher ρ\rho and ρ3\rho_3 mesons

In this work, we systematically study the two-body strong decay of the $\rho/\rho_3$ states, which are observed and grouped into the $\rho/\rho_3$ meson family. By performing the phenomenological analysis, the underlying properties of these states are obtained and tested. What is more important is that abundant information of their two-body strong decays is predicted, which will be helpful to further and experimentally study these states.Comment: 13 pages, 10 figures, 6 tables. Accepted by Phys. Rev.

Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.Comment: 8 pages, 6 figures, MNRAS, in the pres

Prediction of a missing higher charmonium around 4.26 GeV in J/ψJ/\psi family

Inspired by the similarity of mass gaps of $J/\psi$ and $\Upsilon$ families, the prediction of missing higher charmonium with mass $4263$ MeV and very narrow width is made. In addition, the properties of two charmonium-like states, $X(3940)$ and $X(4160)$, and charmonium $\psi(4415)$ are discussed. Here, $X(3940)$ as $\eta_c(3S)$ is established while the explanation of $X(4160)$ to be $\eta_c(4S)$ is fully excluded and $\eta_c(4S)$ is typically a very narrow state. These predictions can be accessible at BESIII, Belle and BelleII in near future.Comment: 5 pages, 5 figures and 1 table. More discussions added. Accepted by Eur. Phys. J.