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

Large Deviations for Stochastic Differential Equations Driven by Semimartingales

We prove the large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of the characteristics of driven semimartingales so that if the noise-control pairs satisfy the large deviation principle with some good rate function, so do the solution processes. There is no exponentially tight assumption for the solution processes