New physics searches at kaon and hyperon factories.

Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons benefit from their small total decay widths and the availability of very large datasets. On the other hand, useful complementary information is provided by hyperon decay measurements. We summarize the relevant phenomenological models and the status of the searches in a comprehensive list of kaon and hyperon decay channels. We identify new search strategies for under-explored signatures, and demonstrate that the improved sensitivities from current and next-generation experiments could lead to a qualitative leap in the exploration of light dark sectors.

Standard-Model Prediction of ε_{K} with Manifest Quark-Mixing Unitarity.

The parameter ε_{K} describes CP violation in the neutral kaon system and is one of the most sensitive probes of new physics. The large uncertainties related to the charm-quark contribution to ε_{K} have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the |ΔS=2| weak effective Lagrangian in which the short-distance theory uncertainty of the imaginary part is dramatically reduced. The uncertainty related to the charm-quark contribution is now at the percent level. We present the updated standard-model prediction ε_{K}=2.16(6)(8)(15)×10^{-3}, where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.

Next-to-next-to-leading-order charm-quark contribution to the CP violation parameter ϵ(K) and ΔM(K).

The observables ϵ(K) and ΔM(K) play a prominent role in particle physics due to their sensitivity to new physics at short distances. To take advantage of this potential, a firm theoretical prediction of the standard-model background is essential. The charm-quark contribution is a major source of theoretical uncertainty. We address this issue by performing a next-to-next-to-leading-order QCD analysis of the charm-quark contribution η(cc) to the effective |ΔS|=2 Hamiltonian in the standard model. We find a large positive shift of 36%, leading to η(cc)=1.87(76). This result might cast doubt on the validity of the perturbative expansion; we discuss possible solutions. Finally, we give an updated value of the standard-model prediction for |ϵ(K)|=1.81(28)×10(-3) and ΔM(K)(SD)=3.1(1.2)×10(-15) GeV.