Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.Comment: 28 Pages; 2 figure

A novel explanation of charmonium-like structure in e+e−→ψ(2S)π+π−e^+e^-\to \psi(2S)\pi^+\pi^-

We first present a non-resonant description to charmonium-like structure $Y(4360)$ in the $\psi(2S)\pi^+\pi^-$ invariant mass spectrum of the $e^+e^-\to \psi(2S)\pi^+\pi^-$ process. The $Y(4360)$ structure is depicted well by the interference effect of the production amplitudes of $e^{+} e^{-} \to \psi(2S) \pi^+ \pi^-$ via the intermediate charmonia $\psi(4160)/\psi(4415)$ and direct $e^+e^-$ annihilation into $\psi(2S)\pi^+ \pi^-$. This fact shows that $Y(4360)$ is not a genuine resonance, which naturally explains why $Y(4360)$ was only reported in its hidden-charm decay channel $\psi(2S)\pi^+\pi^-$ and was not observed in the exclusive open-charm decay channel or $R$-value scan.Comment: 4 pages, 1 table, 2 figures. Accepted for publication in Phys. Rev.

Annihilation Rates of Heavy 1−−1^{--} S-wave Quarkonia in Salpeter Method

The annihilation rates of vector $1^{--}$ charmonium and bottomonium $^3S_1$ states $V \rightarrow e^+e^-$ and $V\rightarrow 3\gamma$, $V \rightarrow \gamma gg$ and $V \rightarrow 3g$ are estimated in the relativistic Salpeter method. We obtained $\Gamma(J/\psi\rightarrow 3\gamma)=6.8\times 10^{-4}$ keV, $\Gamma(\psi(2S)\rightarrow 3\gamma)=2.5\times 10^{-4}$ keV, $\Gamma(\psi(3S)\rightarrow 3\gamma)=1.7\times 10^{-4}$ keV, $\Gamma(\Upsilon(1S)\rightarrow 3\gamma)=1.5\times 10^{-5}$ keV, $\Gamma(\Upsilon(2S)\rightarrow 3\gamma)=5.7\times 10^{-6}$ keV, $\Gamma(\Upsilon(3S)\rightarrow 3\gamma)=3.5\times 10^{-6}$ keV and $\Gamma(\Upsilon(4S)\rightarrow 3\gamma)=2.6\times 10^{-6}$ keV. In our calculations, special attention is paid to the relativistic correction, which is important and can not be ignored for excited $2S$, $3S$ and higher excited states.Comment: 10 pages,2 figures, 5 table