Abstract
The observable epsilon_K is sensitive to flavor violation at some of the highest scales. While its experimental uncertainty is at the half percent level, the theoretical one is in the ballpark of 15%. We explore the nontrivial dependence of the theory prediction and uncertainty on various conventions, like the phase of the kaon fields. In particular, we show how such a rephasing allows to make the short-distance contribution of the box diagram with two charm quarks, eta_cc, purely real. Our results allow to slightly reduce the total theoretical uncertainty of epsilon_K, while increasing the relative impact of the imaginary part of the long distance contribution, underlining the need to compute it reliably. We also give updated bounds on the new physics operators that contribute to epsilon_K.
Highlights
Besides |Vcb|, the largest uncertainty in the SM prediction for K originates from the calculation of ηcc, the QCD correction to the box diagram with two charm quarks
While its experimental uncertainty is at the half percent level, the theoretical one is in the ballpark of 15%
To what extent ηcc is determined by short distance physics may be questioned
Summary
Measures CP violation in mixing, in the limit when Aπ+ −ν = Aπ− +ν = 0 and |Aπ− +ν | = |Aπ+ −ν| Note that these assumptions, valid in the SM to great accuracy, are not precisely tested yet, as the ratio x+ = A(K0 → π− +ν)/A(K0 → π+ −ν) is only constrained at the 10−3 level [3].3. Valid in the SM to great accuracy, are not precisely tested yet, as the ratio x+ = A(K0 → π− +ν)/A(K0 → π+ −ν) is only constrained at the 10−3 level [3].3 In this limit, the definition in eq (2.13), and solving the eigenvalue equations imply. In K0 mixing, the use of chiral perturbation theory, and the separate estimation of short and long distance contributions obscure the cancellations.) The conventions that lead to the “usual” K formula is reviewed in the rest of this section.
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