Possible solution of the puzzle for the branching ratio and CPCP violation in B→ππB\to \pi\pi decays with a modified PQCD approach

We study $B\to \pi\pi$ decay with a modified perturbative QCD approach. The branching ratios and $CP$ violation are calculated with the transverse momenta of partons considered. Sudakov factor associated with each meson is included to suppress soft contribution in QCD. With the wave function of $B$ meson obtained in QCD inspired relativistic potential model being used, the suppression of Sudakov factor to the soft contribution is not effective enough. Soft scale cutoff and soft form factors of $B\pi$ transition and $\pi\pi$ production have to be introduced. The main next-to-leading-order contributions of vertex correction, the quark-loop and magnetic penguin are included. To solve the long-standing puzzle in $B\to\pi\pi$ decay, that is the theoretical prediction of the branching ratio of $B^0\to \pi^0\pi^0$ being seriously smaller than experimental data, color-octet matrix element which is of long-distance dynamics is introduced. With parameters taken with reasonable values, all the branching ratios and $CP$ violation are well consistent with experimental data.Comment: 13 pages, 1 figur

On the pinning strategy of complex networks

In pinning control of complex networks, a tacit believing is that the system dynamics will be better controlled by pinning the large-degree nodes than the small-degree ones. Here, by changing the number of pinned nodes, we find that, when a significant fraction of the network nodes are pinned, pinning the small-degree nodes could generally have a higher performance than pinning the large-degree nodes. We demonstrate this interesting phenomenon on a variety of complex networks, and analyze the underlying mechanisms by the model of star networks. By changing the network properties, we also find that, comparing to densely connected homogeneous networks, the advantage of the small-degree pinning strategy is more distinct in sparsely connected heterogenous networks

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

Abstract not availableZehui Mao, Bin Jiang, Peng Sh