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.

Weak annihilation and new physics in charmless [Formula: see text] decays.

We use currently available data of nonleptonic charmless 2-body [Formula: see text] decays ([Formula: see text]) that are mediated by [Formula: see text] QCD- and QED-penguin operators to study weak annihilation and new-physics effects in the framework of QCD factorization. In particular we introduce one weak-annihilation parameter for decays related by [Formula: see text] quark interchange and test this universality assumption. Within the standard model, the data supports this assumption with the only exceptions in the [Formula: see text] system, which exhibits the well-known "[Formula: see text] puzzle", and some tensions in [Formula: see text]. Beyond the standard model, we simultaneously determine weak-annihilation and new-physics parameters from data, employing model-independent scenarios that address the "[Formula: see text] puzzle", such as QED-penguins and [Formula: see text] current-current operators. We discuss also possibilities that allow further tests of our assumption once improved measurements from LHCb and Belle II become available.

B(s,d)→ℓ(+)ℓ(-) in the standard model with reduced theoretical uncertainty.

We combine our new results for the O(αem) and O(αs2) corrections to Bs,d→ℓ+ℓ-, and present updated branching ratio predictions for these decays in the standard model. Inclusion of the new corrections removes major theoretical uncertainties of perturbative origin that have just begun to dominate over the parametric ones. For the recently observed muonic decay of the Bs meson, our calculation gives B¯(Bs→µ+µ-)=(3.65±0.23)×10-9.

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.

Charm-quark contribution to KL-->mu+mu- at next-to-next-to-leading order.

We calculate the charm-quark contribution to the decay K(L)-->mu(+)mu(-) in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P(c) from +/-22% down to +/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in the short-distance part of the branching ratio and the determination of the Wolfenstein parameter rho[over] from K(L)-->mu(+)mu(-) The error in P(c)=0.115+/-0.018 is now in equal shares due to the combined scale uncertainties and the current uncertainty in the charm-quark mass. We find B(K(L)-->mu(+)mu(-)) SD=(0.79+/-0.12)x10(-9), with the present uncertainty in the Cabibbo-Kobayashi-Maskawa element V(td) being the dominant individual source in the quoted error.

Three-loop mixing of dipole operators.

We calculate the complete three-loop O(alpha(3)(s)) anomalous dimension matrix for the dimension-five dipole operators that arise in the standard model after integrating out the top quark and the heavy electroweak bosons. Our computation completes the three-loop anomalous dimension matrix of operators that govern low-energy |DeltaF| = 1 flavor-changing processes, and represents an important ingredient of the next-to-next-to-leading order QCD analysis of the B--> X(s)gamma decay.

Rare decay K+ --> pi+ nunu at the next-to-next-to-leading order in QCD.

We calculate the charm quark contribution to the rare decay Kappa(+)--> pi(+) nunu in the next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter Pc from +/-10.1% down to +/-2.4%, corresponding to scale uncertainties of +/-1.3%, +/-1.0%, +/-0.006, and +/-1.2 degrees in Beta(Kappa(+) --> pi(+) nunu) and in |V(td)|, sin2(Beta), and gamma extracted from the Kappa --> pinunu system. The error in Rho(c) = 0.37 +/- 0.04 is now fully dominated by the current uncertainty of +/-3.8% in the charm quark mass m(c). We find Beta(Kappa(+) --> pi(+)nunu) = (8.0 +/- 1.1) x 10(-11), where the quoted error stems almost entirely from the present uncertainties in m(c) and the Cabibbo-Kobayashi-Maskawa elements.