Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter epsilon_K and Delta M_K

TL;DR

This paper performs a detailed NNLO QCD analysis of the charm-quark contribution to key kaon observables, reducing theoretical uncertainties and updating the standard-model predictions for epsilon_K and Delta M_K.

Contribution

It provides the first NNLO calculation of eta_cc, significantly refining the theoretical prediction of kaon mixing parameters in the standard model.

Findings

Eta_cc increased by 36% at NNLO

Updated epsilon_K value: 1.81(28) x 10^-3

Updated Delta M_K(SD): 3.1(1.2) x 10^-15 GeV

Abstract

The observables epsilon_K and Delta M_K play a prominent role in particle physics due to their sensitivity to new physics at short distances. To take advantage of this potential, a firm theoretical prediction of the standard-model background is essential. The charm-quark contribution is a major source of theoretical uncertainty. We address this issue by performing a next-to-next-to-leading-order (NNLO) QCD analysis of the charm-quark contribution eta_cc to the effective |Delta S|=2 Hamiltonian in the standard model. We find a large positive shift of 36%, leading to eta_cc = 1.87(76). This result might cast doubt on the validity of the perturbative expansion; we mention possible solutions. Finally, we give an updated value of the standard-model prediction for |epsilon_K| = 1.81(28) x 10^-3 and Delta M_K(SD) = 3.1(1.2) x 10^-15 GeV.