Circle bundles over 4-manifolds

Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by #_{r-1}S^{2}\times S^{3}, where $r=$rankH^{2}(M;\QTR{Bbb}{Z}).Comment: 6 pages to appear in Archiv der Mat

Trapped ion quantum computation with transverse phonon modes

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.Comment: 5 page

Study of the quasi-two-body decays B^{0}_{s} \rightarrow \psi(3770)(\psi(3686))\pi^+\pi^- with perturbative QCD approach

In this note, we study the contributions from the S-wave resonances, f_{0}(980) and f_{0}(1500), to the B^{0}_{s}\rightarrow \psi(3770)\pi^ {+}\pi^{-} decay by introducing the S-wave \pi\pi distribution amplitudes within the framework of the perturbative QCD approach. Both resonant and nonresonant contributions are contained in the scalar form factor in the S-wave distribution amplitude \Phi^S_{\pi\pi}. Since the vector charmonium meson \psi(3770) is a S-D wave mixed state, we calculated the branching ratios of S-wave and D-wave respectively, and the results indicate that f_{0}(980) is the main contribution of the considered decay, and the branching ratio of the \psi(2S) mode is in good agreement with the experimental data. We also take the S-D mixed effect into the B^{0}_{s}\rightarrow \psi(3686)\pi^ {+}\pi^{-} decay. Our calculations show that the branching ratio of B^{0}_{s}\rightarrow \psi(3770)(\psi(3686))\pi^ {+}\pi^{-} can be at the order of 10^{-5}, which can be tested by the running LHC-b experiments.Comment: 10 pages, 3 figure