Standard model evaluation of εK using lattice QCD inputs for B^K and Vcb

We report the standard model evaluation of the indirect CP violation parameter εK using inputs determined from lattice QCD: the kaon bag parameter B^K, ξ0, |Vus| from the Kℓ3 and Kμ2 decays, and |Vcb| from the axial current form factor for the exclusive decay B¯→D∗ℓν¯ at zero-recoil. The theoretical expression for εK is thoroughly reviewed to give an estimate of the size of the neglected corrections, including long distance effects. The Wolfenstein parametrization (|Vcb|,λ,ρ¯,η¯) is adopted for Cabibbo-Kobayashi-Maskawa matrix elements which enter through the short distance contribution of the box diagrams. For the central value, we take the unitarity triangle apex (ρ¯,η¯) from the angle-only fit of the UTfit collaboration and use Vus as an independent input to fix λ. We find that the standard model prediction of εK with exclusive Vcb (lattice QCD results) is lower than the experimental value by 3.4σ. However, with inclusive Vcb (results of the heavy quark expansion), there is no gap between the standard model prediction of εK and its experimental value. For the calculation of εK, we perform the renormalization group running to obtain ηcc at next-to-next-to-leading-order; we find ηccNNLO=1.72(27).