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The rare K → πνν decays play a central role in testing the Standard Model and its extensions. Upcoming experiments plan to measure the decay rates with high accuracy. Yet, unknown higher-order electroweak corrections result in a sizeable theory error. We remove this uncertainty by computing the full two-loop electroweak corrections to the top-quark contribution X t to the rare decays K L → π 0 νν, K + → π + νν, and B → X d,s νν in the Standard Model. The remaining theoretical uncertainty related to electroweak effects is now far below 1%. Finally we update the branching ratios to find Br(K L → π 0 νν) = 2.43(39)(6) × 10 −11 and Br(K + → π + νν) = 7.81(75)(29) × 10 −11 . The first error summarises the parametric, the second the remaining theoretical uncertainties.

In the past decade, one of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor. In this time frame, measurements and the theoretical interpretation of their results have advanced tremendously. A much broader understanding of flavor particles has been achieved; apart from their masses and quantum numbers, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. In the past, observations of CP violation were confined to neutral K mesons, but since the early 1990s, a large number of CP-violating processes have been studied in detail in neutral B mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of K, D, and B mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments; thus a review of the status of quark flavor physics is timely. This report is the result of the work of physicists attending the 5th CKM workshop, hosted by the University of Rome "La Sapienza", September 9-13, 2008. It summarizes the results of the current generation of experiments that are about to be completed and it confronts these results with the theoretical understanding of the field which has greatly improved in the past decade. (C) 2010 Elsevier B.V. All rights reserved