The Kostant invariant and special ϵ-orthogonal representations for ϵ-quadratic colour Lie algebras

A weight basis for representations of even orthogonal Lie algebras

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand–Tsetlin patterns. The basis is consistent with the chain of subalgebras g1 ⊂ · · · ⊂ gn, where gk = o(2k). Explicit formulas for the matrix elements of generators of o(2n) in this basis are given. The construction is b...

The Standard Model Prediction for ε′/ε

We present a detailed analysis of ε/ε within the Standard Model, taking into account the strong enhancement through final–state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/NC expansion, through a matching procedure between the effective short–distance Lagrangian and its corresponding low–energy description in Chiral Per...

Invariant Points and ε-Simultaneous Approximation

DAGmaps and ε-Visibility Representations of DAGs

DAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NP-complete. Recently we defined a special case called one-dimensional DAGmap where the admissibility is decided in linear time. However there is no complete characterization of the class of DAGs that admit a onedimensional DAGmap. In this paper we prove that a DAG admits ...

ε′/ε and Chiral Dynamics

The long-distance contributions to K → 2π amplitudes can be pinned down, using well established Chiral Perturbation Theory techniques. The strong S–wave rescattering of the two final pions generates sizeable chiral loop corrections, which have an important impact on the direct CP violation ratio ε/ε [1,2]. Including all large logarithmic corrections, both at short and long distances, the Standa...