A new look at the theory uncertainty of epsilon_K

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.