Branching Ratio and Polarization of B→ρ(ω)ρ(ω)B\to\rho(\omega)\rho(\omega) Decays in Perturbative QCD Approach

In this work, we calculated the branching ratios, polarization fractions and CP asymmetry of decay modes $B\to\rho(\omega)\rho(\omega)$ in the Perturbative QCD approach, which is based on $\mathbf{k}_T$ factorization. After calculation, we find the the branching ratios of $B^0 \to \rho^+ \rho^-$, $B^+ \to \rho^+ \rho^0$ and $B^+ \to \rho^+ \omega$ are at the order of $10^{-5}$, and their longitudinal polarization fractions are more than 90%. The above results agree with BarBar's measurements. We also predict the branching ratios and polarizations of $B^0 \to \rho^0 \rho^0$, $B^0 \to \rho^0 \omega$ and $B^0 \to \omega \omega$, which will be measured in future. We predicted the CP asymmetry of $B^0 \to \rho^+ \rho^-$ and $B^+ \to \rho^+ \rho^0$, which will play important role in determining angle $\alpha$.Comment: 13 pages, 4 figure

Analysis and evaluation of the entropy indices of a static network structure

Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.The authors would like to thank the financial support of the National Natural Science Foundation of China (71501153), Natural Science Foundation of Shaanxi Province of China (2016JQ6072), and the Foundation of China Scholarship Council (201506965039, 201606965057). (71501153 - National Natural Science Foundation of China; 2016JQ6072 - Natural Science Foundation of Shaanxi Province of China; 201506965039 - Foundation of China Scholarship Council; 201606965057 - Foundation of China Scholarship Council)Published versio

Intrinsic Regularization Method in QCD

There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization method, to regularize those divergent graphs. In this paper, we apply this method to QCD at the one loop order. It turns out to be satisfactory:The gauge invariance is preserved manifestly and the results are the same as those derived by means of other regularization methods.Comment: 18 pages, LaTeX , 7 figures in a separate compressed postscript fil