Light Hadron Weak Matrix Elements

Weak processes involving light hadrons in general, and kaons in particular, have contributed significantly to our understanding of fundamental interactions over the years. Most recently, the measurement of a non-vanishing Re ǫ/ǫ in K → ππ decays by KTeV [1] and NA48 [2] has provided unambiguous evidence for direct CP violation. In constraining the Standard Model (SM), the physics of kaons is complementary to that of B mesons. This is clearly visible in Figure 1, where the types of constraints imposed by weak processes involving either of these particles are displayed. Kaons provide an important constraint on the summit of the unitarity triangle through the measurement of ǫ, the parameter which quantifies indirect CP violation in K → ππ decays. This constraint requires a description of non-perturbative effects in K0−K̄0 mixing, parametrized by BK . Lattice results for this quantity are commonly used in unitarity triangle fits. There are two new results this year for BK , obtained with domain-wall fermions, by the CP-PACS [3] and RBC [4] collaborations. Rare kaon decays and other FCNC kaon processes also provide good probes of physics beyond the SM. Here too the lattice is contributing. Donini et al. have computed SUSY, ∆S = 2 matrix elements [5] and the SPQcdR collaboration have performed the first lattice determination of the electromagnetic operator matrix element, 〈π|Qγ |K0〉, which contributes to enhance the CP violating component of theKL → πee amplitude in SUSY extensions of the SM [6,7]. The need for a non-perturbative technique such K L νν 0 π K L π 0 e e + -