$ε^{\prime}/ε$ at the next-to-leading order in QCD and QED

Abstract

We present a new calculation of the CP violation parameter $ε^{\prime}/ ε$. The results reported in this paper have been obtained by using the $ΔS=1$ effective Hamiltonian computed at the next-to-leading order, including QCD and QED penguins. The matrix elements of the relevant operators have been taken from lattice QCD, at a scale $μ=2$ GeV. At this relatively large scale, the perturbative matching between the relevant operators and the corresponding coefficients is quite reliable. The effect of the next-to-leading corrections is to lower the prediction obtained at the leading order, thus favouring the experimental result of E731. We analyze different contributions to the final result and compare the leading and next-to-leading cases.