Abstract
We present the calculation of the short-distance power corrections to the CP-violation parameter εK coming from dimension-8 operators in the ∆S = 2 effective Hamiltonian. A first estimate of this contribution, obtained for large-Nc and in the chiral limit, was provided in ref. [1]. Here we evaluate and include the mathcal{O}left({m}_K^2/{m}_c^2right) and mathcal{O}left({Lambda}_{mathrm{QCD}}^2/{m}_c^2right) contributions that, a priori, could induce mathcal{O} (1) corrections to previous estimates, as mK is numerically of order ΛQCD. Our computation shows that there are several dimension-8 operators besides the one considered before. Their effect on εK, however, accidentally cancels out to a large extent, leaving the final correction at the level of 1%.
Highlights
Corrections to the Wilson coefficients of the ∆S = 2 effective Hamiltonian [10, 11]
We present the calculation of the short-distance power corrections to the CP-violation parameter εK coming from dimension-8 operators in the ∆S = 2 effective Hamiltonian
While the NNLO result for the Wilson coefficients is a crucial step to reduce the theoretical uncertainty of εK, at present there is no gain in evaluating the Wilson coefficient with NNLO accuracy when the accuracy of the matrix element is only at NLO: the overall uncertainty on εK remains at the NLO level in any case
Summary
The calculation of the δmc is based on the determination of the Wilson coefficients of dimension-8 operators from matching conditions To this aim, box diagrams have to be calculated with non vanishing external quark momenta. A, coming from the double insertion of the effective ∆S = 1 Hamiltonian, whereas the last term is the contribution that can be expressed as linear combination of local operators multiplied by suitable Wilson coefficients CiW. The contribution to the mixing amplitude of the double penguin diagrams of figures 2 corresponds to the long distance corrections to εK estimated in ref.
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