The puzzles in B→ππB\to \pi\pi and πK \pi K decays: possible implications for R-parity violating supersymmetry

Recent experiments suggest that certain data of $B \to \pi\pi,\pi K$ decays are inconsistent with the standard model expectations. We try to explain the discrepancies with R-parity violating suppersymmetry. By employing the QCD factorization approach, we study these decays in the minimal supersymmetric standard model with R-parity violation. We show that R-parity violation can resolve the discrepancies in both $B \to \pi\pi$ and $B \to \pi K$ decays, and find that in some regions of parameter spaces all these requirements, including the CP averaged branching ratios and the direct CP asymmetries, can be satisfied. Furthermore, we have derived stringent bounds on relevant R-parity violating couplings from the latest experimental data, and some of these constraints are stronger than the existing bounds.Comment: 24 pages, 6 figures and 5 tables. Text revised. Final version to appear in PR

Computing a matrix function for exponential integrators

AbstractAn efficient numerical method is developed for evaluating ϕ(A), where A is a symmetric matrix and ϕ is the function defined by ϕ(x)=(ex−1)/x=1+x/2+x2/6+⋯. This matrix function is useful in the so-called exponential integrators for differential equations. In particular, it is related to the exact solution of the ODE system dy/dt=Ay+b, where A and b are t-independent. Our method avoids the eigenvalue decomposition of the matrix A and it requires about 10n3/3 operations for a general symmetric n×n matrix. When the matrix is tridiagonal, the required number of operations is only O(n2) and it can be further reduced to O(n) if only a column of the matrix function is needed. These efficient schemes for tridiagonal matrices are particularly useful when the Lanczos method is used to calculate the product of this matrix function (for a large symmetric matrix) with a given vector

Polarizations in decays B_{u,d}\to VV and possible implications for R-parity violating SUSY

Recently BABAR and Belle have measured anomalous large transverse polarizations in some pure penguin $B \to VV$ decays, which might be inconsistent with the Standard Model expectations. We try to explore its implications for R-parity violating (RPV) supersymmetry. The QCD factorization approach is employed for the hadronic dynamics of B decays. We find that it is possible to have parameter spaces solving the anomaly. Furthermore, we have derived stringent bounds on relevant RPV couplings from the experimental data, which is useful for further studies of RPV phenomena.Comment: 26 pages, 12 eps figures. Typos corrected and references added. Final version to appear in PR

Moment matching technique for fast and robust uncertainty quantifications of complex systems

Despite the growing popularity of reinforced concrete (RC) core walls, robust uncertainty quantification of their global and local performances remains an intractable challenge. A combination of a random sampling technique in conjunction with a simplified structural analysis has been widely used, but substantial ambiguity remains in the simulation accuracy and the resultant uncertainties. As a fast and robust alternative, this study suggests a moment matching (MM) technique. MM can dramatically reduce required sample points to only a few, which enables a direct use of a high-precision parallel multiscale finite element analysis (PM-FEA) for uncertainty quantification. This study demonstrates how to apply the combination of MM and PM-FEA to quantify uncertainties behind complex RC core walls, notably in terms of global force-resisting capacity and microscopic progressive bar buckling of five U-shaped walls. Results suggest that the combination of MM and PM-FEA will serve as a promising method to improve our understanding of uncertainties behind complex RC structure