The known isospin-breaking contributions to the K → ππ amplitudes are reanalyzed, taking into account our current understanding of the quark masses and the relevant non-perturbative inputs. We present a complete numerical reappraisal of the direct CP-violating ratio / , where these corrections play a quite significant role. We obtain the Standard Model prediction Re ( / ) = (14 ± 5) · 10 −4 , which is in very good agreement with the measured ratio. The uncertainty, which has been estimated conservatively, is dominated by our current ignorance about 1/N C -suppressed contributions to some relevant chiral-perturbation-theory low-energy constants.
In 1988 the NA31 experiment presented the first evidence of direct CP violation in the [Formula: see text] decay amplitudes. A clear signal with a [Formula: see text] statistical significance was later established with the full data samples from the NA31, E731, NA48 and KTeV experiments, confirming that CP violation is associated with a [Formula: see text] quark transition, as predicted by the Standard Model. However, the theoretical prediction for the measured ratio [Formula: see text] has been a subject of strong controversy along the years. Although the underlying physics was already clarified in 2001, the recent release of improved lattice data has revived again the theoretical debate. We review the current status, discussing in detail the different ingredients that enter into the calculation of this observable and the reasons why seemingly contradictory predictions were obtained in the past by several groups. An update of the Standard Model prediction is presented and the prospects for future improvements are analysed. Taking into account all known short-distance and long-distance contributions, one obtains [Formula: see text], in good agreement with the experimental measurement.
Rare |∆c| = |∆u| = 1 transitions into dineutrinos are strongly GIM-suppressed and constitute excellent null tests of the standard model. While branching ratios of D → P ν ν, D → P + P − ν ν, P = π, K, baryonic Λ + c → p ν ν, and Ξ + c → Σ + ν ν and inclusive D → Xν ν decays are experimentally unconstrained, signals of new physics can be just around the corner. We provide model-independent upper limits on branching ratios reaching few ×10 −5 in the most general case of arbitrary lepton flavor structure, ∼ 10 −5 for scenarios with charged lepton conservation and few ×10 −6 assuming lepton universality. We also give upper limits in Z and leptoquark models. The presence of light right-handed neutrinos can affect these limits, a possibility that can occur for lepton number violation at a TeV, and that can be excluded with an improved bound on B(D 0 → invisibles) at the level of ∼ 10 −6 , about two orders of magnitude better than the present one. Signatures of c → uν ν modes contain missing energy and are suited for experimental searches at e + e − -facilities, such as BES III, Belle II and future e + e − -colliders, such as the FCC-ee running at the Z.
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