The analysis of the charmonium-like states X∗(3860)X^{*}(3860),X(3872)X(3872), X(3915)X(3915), X(3930)X(3930) and X(3940)X(3940) according to its strong decay behaviors

Inspired by the newly observed state $X^{*}(3860)$, we analyze the strong decay behaviors of some charmonium-like states $X^{*}(3860)$,$X(3872)$, $X(3915)$, $X(3930)$ and $X(3940)$ by the $^{3}P_{0}$ model. We carry out our work based on the hypothesis that these states are all being the charmonium systems. Our analysis indicates that $0^{++}$ charmonium state can be a good candidate for $X^{*}(3860)$ and $1^{++}$ state is the possible assignment for $X(3872)$. Considering as the $3^{1}S_{0}$ state, the decay behavior of $X(3940)$ is inconsistent with the experimental data. So, we can not assign $X(3940)$ as the $3^{1}S_{0}$ charmonium state by present work. Besides, our analysis imply that it is reasonable to assign $X(3915)$ and $X(3930)$ to be the same state, $2^{++}$. However, combining our analysis with that of Zhou~\cite{ZhouZY}, we speculate that $X(3915)$/$X(3930)$ might not be a pure $c\overline{c}$ systems

Fine gradings of complex simple Lie algebras and Finite Root Systems

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading. Analogous to classical root systems, we define a finite root system $R$ to be some subset of a finite symplectic abelian group satisfying certain axioms. There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a quasi-good grading on it. Thus one can construct nice basis of $L(R)$ by means of finite root systems. We classify finite maximal abelian subgroups $T$ in \Aut(L) for complex simple Lie algebras $L$ such that the grading induced by the action of $T$ on $L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always a finite root system. There are five series of such finite maximal abelian subgroups, which occur only if $L$ is a classical simple Lie algebra

Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the ${\delta}$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the ${\delta}$-function, and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the ${\delta}$-function.Comment: v1: 25 pages, 14 figures; v2: 26 pages, 15 figures; v3: minor revisions, final version to appear in Adv. High Energy Phy

Strong coupling constants and radiative decays of the heavy tensor mesons

In this article, we analyze tensor-vector-pseudoscalar(TVP) type of vertices $D_{2}^{*+}D^{+}\rho$, $D_{2}^{*0}D^{0}\rho$, $D_{2}^{*+}D^{+}\omega$, $D_{2}^{*0}D^{0}\omega$, $B_{2}^{*+}B^{+}\rho$, $B_{2}^{*0}B^{0}\rho$, $B_{2}^{*+}B^{+}\omega$, $B_{2}^{*0}B^{0}\omega$, $B_{s2}^{*}B_{s}\phi$ and $D_{s2}^{*}D_{s}\phi$, in the frame work of three point QCD sum rules. According to these analysis, we calculate their strong form factors which are used to fit into analytical functions of $Q^{2}$. Then, we obtain the strong coupling constants by extrapolating these strong form factors into deep time-like regions. As an application of this work, the coupling constants for radiative decays of these heavy tensor mesons are also calculated at the point of $Q^{2}=0$. With these coupling constants, we finally calculate the radiative decay widths of these tensor mesons.Comment: arXiv admin note: text overlap with arXiv:1810.0597

Analysis of the strong coupling form factors of ΣbNB\Sigma_bNB and ΣcND\Sigma_c ND in QCD sum rules

In this article, we study the strong interaction of the vertexes $\Sigma_bNB$ and $\Sigma_c ND$ using the three-point QCD sum rules under two different dirac structures. Considering the contributions of the vacuum condensates up to dimension $5$ in the operation product expansion, the form factors of these vertexes are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant. Our analysis indicates that the coupling constant for these two vertexes are $G_{\Sigma_bNB}=0.43\pm0.01GeV^{-1}$ and $G_{\Sigma_cND}=3.76\pm0.05GeV^{-1}$.Comment: 6 figure