Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter εK and ΔMK

The observables epsilon K and epsilon 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 QCD analysis of the charm-quark contribution eta(cc) to the effective vertical bar Delta S vertical bar = 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 discuss possible solutions. Finally, we give an updated value of the standard-model prediction for vertical bar epsilon(K)vertical bar = 1.81(28) X 10(-3) and Delta M-K(SD) 3.1d(1.2) X 10(-15) GeV.