B→SB\to S Transition Form Factors in the PQCD approach

Under two different scenarios for the light scalar mesons, we investigate the transition form factors of $B(B_s)$ mesons decay into a scalar meson in the perturbative QCD approach. In the large recoiling region, the form factors are dominated by the short-distance dynamics and can be calculated using perturbation theory. We adopt the dipole parametrization to recast the $q^2$ dependence of the form factors. Since the decay constants defined by the scalar current are large, our predictions on the $B\to S$ form factors are much larger than the $B\to P$ transitions, especially in the second scenario. Contributions from various light-cone distribution amplitudes (LCDAs) are elaborated and we find that the twist-3 LCDAs provide more than a half contributions to the form factors. The two terms of the twist-2 LCDAs give destructive contributions in the first scenario while they give constructive contributions in the second scenario. With the form factors, we also predict the decay width and branching ratios of the semileptonic $B\to Sl\bar\nu$ and $B\to Sl^+l^-$ decays. The branching ratios of $B\to Sl\bar\nu$ channels are found to have the order of $10^{-4}$ while those of $B\to Sl^+l^-$ have the order of $10^{-7}$. These predictions can be tested by the future experiments.Comment: 20 pages, 31 figure

Branching Ratios, Forward-backward Asymmetry and Angular Distributions of B→K1l+l−B\to K_1l^+l^- Decays

Using the $B\to K_1$ form factors evaluated in the perturbative QCD approach, we study semileptonic $B\to K_1(1270)l^+l^-$ and $B\to K_1(1400)l^+l^-$ decays, where $K_1(1270)$ and $K_1(1400)$ are mixtures of $K_{1A}$ and $K_{1B}$ which are $^3P_1$ and $^1P_1$ states, respectively. Using the technique of helicity amplitudes, we express the decay amplitudes in terms of several independent and Lorentz invariant pieces. We study the dilepton invariant mass distributions, branching ratios, polarizations and forward-backward asymmetries of $B\to K_1l^+l^-$ decays. The ambiguity in the sign of the mixing angle will induce much large differences to branching ratios of semileptonic B decays: branching ratios without resonant contributions either have the order of $10^{-6}$ or $10^{-8}$. But the polarizations and the forward-backward asymmetries are not sensitive to the mixing angles. We find that the resonant contributions will dramatically change the dilepton invariant mass distributions in the resonant region. We also provide the angular distributions of $B\to K_1l^+l^-\to (K\pi\pi)l^+l^-$ decays.Comment: 14 pages, 6 figures, version appears in PR

Cascading failures in coupled networks with both inner-dependency and inter-dependency links

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We find that when most of dependency links are inner- or inter-ones, the coupled networks system is fragile and makes a discontinuous percolation transition. However, when the numbers of two types of dependency links are close to each other, the system is robust and makes a continuous percolation transition. This indicates that the high density of dependency links could not always lead to a discontinuous percolation transition as the previous studies. More interestingly, although the robustness of the system can be optimized by adjusting the ratio of the two types of dependency links, there exists a critical average degree of the networks for coupled random networks, below which the crossover of the two types of percolation transitions disappears, and the system will always demonstrate a discontinuous percolation transition. We also develop an approach to analyze this model, which is agreement with the simulation results well.Comment: 9 pages, 4 figure

Research on Dynamic Response of Anchored Jointed Rock Slope under Traffic Load

Based on the actual slope engineering, the dynamic response characteristics of the anchored joint slope in acceleration, velocity, and anchorage cable axial force under traffic load are numerically simulated. The results show that the cable axial force of the anchored slope starts to rise from the anchor head under traffic load, reaches a stable value in the free section, and falls to close to zero in the anchorage section. The axial force of the anchorage cable decreases when the slope height increases. Within the free section of the anchorage cable, there is a "small platform", where the axial force value decreases slightly and rises again, and its position corresponds to the range in which the anchorage cable passes through the joint. The dynamic response of traffic loads to the monitoring points of the slope is related to the magnitude of the load, the frequency, and the duration of the vibration. It is also related to the distance from the location of the traffic load, the physical and mechanical parameters of the location, the existence of joints, cracks and other structural planes, and whether or not to take support measures. When the frequency of the traffic load is close to the natural frequency of the slope, the resonance phenomenon is easy to occur, and the damage of the rock and soil of the slope is increased

The Origin and Characteristics of Family Sports in Germany

Family sports, as a breakthrough of national fitness in Germany, has gone through more than 30 years of development. This study examined the origin, management, operation, guarantee, and promotion mechanism of family sports in Germany by using the methods of literature and field investigation. It is found that family sports in Germany originated from the implementation of Gold Plan in Germany, which has the following characteristics: Taking the top management organization of national sports as the link, paying attention to the coordinated management of family and club; paying attention to the coordination and cooperation of multiple departments and organizations. To integrate social resources, to focus on the responsibility of sports clubs, to create a family sports guide, and to focus on family friendly development model are the mechanism driving force to promote the development of family sports. And get the following enlightenment: give full play to the guiding role of the policy, cultivate all kinds of social organizations to promote the development of family sports; based on the integration model of school, family and community, create a good environment for the development of family sports; create the family sports guide to guide the development of Court Sports in our country; adhere to the family sports development model of family centered

Transition form factors of B decays into p-wave axial-vector mesons in the perturbative QCD approach

The $B_{u,d,s}\to V,A$ form factors are studied in perturbative QCD approach ($V,A$ denote a vector meson and two kinds of p-wave axial-vector mesons: $^3P_1$ and $^1P_1$ states, respectively.). The form factors are directly studied in the large recoiling region and extrapolated to the whole kinematic region within the dipole parametrization. Adopting decay constants with different signs for the two kinds of axial-vectors, we find that the two kinds of $B\to A$ form factors have the same sign. The two strange mesons $K_{1A}$ and $K_{1B}$ mix with each other via the SU(3) symmetry breaking effect. In order to reduce the ambiguities in the mixing angle between $K_{1A}$ and $K_{1B}$, we propose a model-independent way that utilizes the B decay data. Most of the branching fractions of the semilteptonic $B\to Al\bar \nu_l$ decays are of the order $10^{-4}$, which still need experimental tests in the on-going and forthcoming experiments.Comment: 22 pages, 7 figure