Power corrections to the CP-violation parameter $\varepsilon_K$

TL;DR

This paper calculates short-distance power corrections from dimension-8 operators to the CP-violation parameter _K, finding that these corrections largely cancel out, resulting in a small overall impact of about 1%.

Contribution

It provides the first detailed evaluation of _K power corrections from multiple dimension-8 operators, including (m_K^2/m_c^2) and (_{QCD}^2/m_c^2) terms, extending previous estimates.

Findings

Corrections from dimension-8 operators cancel out largely.

The net correction to _K is approximately 1%.

Multiple operators contribute to the correction, but their effects offset each other.

Abstract

We present the calculation of the short-distance power corrections to the CP-violation parameter $\varepsilon_K$ coming from dimension-8 operators in the $\Delta S=2$ effective Hamiltonian. A first estimate of this contribution, obtained for large-$N_c$ and in the chiral limit, was provided in ref. [arXiv:hep-ph/0406094]. Here we evaluate and include the $\mathcal{O}(m_K^2/m_c^2)$ and $\mathcal{O}(\Lambda_{QCD}^2/m_c^2)$ contributions that, a priori, could induce $\mathcal{O}(1)$ corrections to previous estimates, as $m_K$ is numerically of order $\Lambda_{QCD}$. Our computation shows that there are several dimension-8 operators besides the one considered before. Their effect on $\varepsilon_K$, however, accidentally cancels out to a large extent, leaving the final correction at the level of 1%.