A new look at the theory uncertainty of epsilon_K

TL;DR

This paper examines the theoretical uncertainties in the epsilon_K parameter, highlighting how rephasing conventions can reduce these uncertainties and emphasizing the importance of accurately computing long-distance contributions for new physics constraints.

Contribution

It introduces a rephasing method to reduce theoretical uncertainties in epsilon_K and provides updated bounds on new physics operators affecting it.

Findings

Rephasing can make the charm-quark box diagram contribution purely real.

Reduced theoretical uncertainty enhances sensitivity to new physics.

Highlights the importance of computing long-distance contributions accurately.

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.