The structure of f(R)f(R)-brane model

Recently, a family of interesting analytical brane solutions were found in $f(R)$ gravity with $f(R)=R+\alpha R^2$ in Ref. [Phys. Lett. B 729, 127 (2014)]. In these solutions, inner brane structure can be turned on by tuning the value of the parameter $\alpha$. In this paper, we investigate how the parameter $\alpha$ affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of $\alpha$, despite the brane has an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton KK modes has a singular structure, and there exists a series of graviton resonant modes. The contribution of the massive graviton KK modes to the Newton's law of gravity is discussed shortly.Comment: v2: 10 pages, 8 figures, to be published in EPJ

Search for C=+C=+ charmonium and XYZ states in e+e−→γ+He^+e^-\to \gamma+ H at BESIII

Within the framework of nonrelativistic quantum chromodynamics, we study the production of $C=+$ charmonium states $H$ in $e^+e^-\to \gamma~+~H$ at BESIII with $H=\eta_c(nS)$ (n=1, 2, 3, and 4), $\chi_{cJ}(nP)$ (n=1, 2, and 3), and $^1D_2(nD)$ (n=1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for $S$ and $P$ wave states. We then argue that the search for $C=+$ $XYZ$ states such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ in $e^+e^-\to \gamma~+~H$ at BESIII may help clarify the nature of these states. BESIII can search $XYZ$ states through two body process $e^+e^-\to \gamma H$, where $H$ decay to $J/\psi \pi^+\pi^-$, $J/\psi \phi$, or $D \bar D$. This result may be useful in identifying the nature of $C=+$ $XYZ$ states. For completeness, the production of $C=+$ charmonium in $e^+e^-\to \gamma +~H$ at B factories is also discussed.Comment: Comments and suggestions are welcome. References are update