Kaon theory: 50 years later

We summarize the status of the kaon theory 50 years after the seminal paper of Kobayashi and Maskawa [Prog. Theor. Phys. 49, 652 (1973)], who pointed out that six quarks are necessary to have CP violation in the Standard Model (SM) and presented a parametrization of a 3 × 3 unitary matrix that, after the discovery of the charm quark in 1974 and the b quark in 1977, dominated the field of flavor-changing processes. One of the main goals of flavor physics since then has been the determination of the four parameters of this matrix, which we will choose here to be |V_us|, |V_cb|, and the two angles of the unitarity triangle, β and γ, with |V_us| introduced by Cabibbo in 1963. I will summarize the recent strategy for determination of these parameters without new physics (NP) infection. It is based on the conjecture of the absence of relevant NP contributions to ΔF = 2 processes that indeed can be demonstrated by a negative rapid test: the |V_cb|-γplot. This in turn allows one to obtain SM predictions for rare K and B decays that are the most precise to date. We present strategies for the explanation of the anticipated anomaly in the ratio ϵ′/ϵ and the observed anomalies in b → sμ⁺μ^- transitions that are consistent with our ΔF = 2 conjecture. In particular, the absence of NP in the parameter ϵ_K still allows for significant NP effects in ϵ′/ϵ and in rare kaon decays, moreover, in a correlated manner. Similarly, the absence of NP in ΔM_s combined with anomalies in b → sμ⁺μ^- transitions hints at the presence of right-handed quark currents. We also discuss how the nature of neutrinos, Dirac vs. Majorana ones, can be probed in and decays. The present status of the ΔI = 1/2 rule and ϵ′/ϵ is summarized.