CP Violation and Strong Phases from Penguins in B±→VV\bf B^{\pm}\rightarrow VV Decays

We calculate direct CP-violating observables in charged $B\to VV$ decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order $\alpha_s$ from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugate $B^{\pm}$ decays can be as high as 15-30\% for certain channels with branching ratios in the $10^{-6}$ range. The small values of the coefficients of angular correlations, which we calculated previously to be of order $10^{-2}$, are not significantly degraded by the strong phases. The charge asymmetries of rates and angular distributions would provide unambiguous evidence for direct CP violation.Comment: 24 pages, 3 figures (upon request), LaTeX, preprint DESY 93-19

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity