Power corrections to the CP-violation parameter ${\epsilon }_K$

Abstract

We present the calculation of the short-distance power corrections to the CP-violation parameter ${\epsilon }_K$ 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 ${\epsilon }_K$, however, accidentally cancels out to a large extent, leaving the final correction at the level of 1%.

Comments: 23 pages, 2 figures. v2: added references and CKM parameter values. v3: matches published version