Next-to-next-to-leading-order charm-quark contribution to the CP violation parameter ϵ(K) and ΔM(K).

The observables ϵ(K) and ΔM(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 η(cc) to the effective |ΔS|=2 Hamiltonian in the standard model. We find a large positive shift of 36%, leading to η(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 |ϵ(K)|=1.81(28)×10(-3) and ΔM(K)(SD)=3.1(1.2)×10(-15)  GeV.