Abstract
The parameter ϵK measures CP violation in the neutral kaon system. It is a sensitive probe of new physics and plays a prominent role in the global fit of the Cabibbo-Kobabyashi-Maskawa matrix. The perturbative theory uncertainty is currently dominated by the top-quark contribution. Here, we present the calculation of the full two-loop electroweak corrections to the top-quark contribution to ϵK, including the resummation of QED-QCD logarithms. We discuss different renormalization prescriptions for the electroweak input parameters. In the traditional normalization of the weak Hamiltonian with two powers of the Fermi constant GF, the top-quark contribution is shifted by −1%.
Highlights
Neutral kaon mixing are conveniently described by the effective |∆S| = 2 Lagrangian with three active quark flavors, L|f∆=S3|=2
To quantify the impact of the electroweak corrections, we examine the numerical values of the Wilson coefficients in the hybrid renormalization scheme, as it shows the best convergence properties and least residual scale dependence
We have presented the complete two-loop electroweak corrections to the top-quark contribution to the parameter K
Summary
In the SM, the leading-order (LO) contributions to the Wilson coefficients are given by one-loop box diagrams [5]. Higher-order QCD corrections have been calculated in renormalizationgroup (RG) improved perturbation theory, using a slightly different representation of the. |∆S| = 2 effective Lagrangian [6], in terms of λc and λt It was shown recently [7] that the parameterization (1.2) in terms of λu and λt leads to a perturbative QCD uncertainty smaller by an order of magnitude. We will adopt this parameterization in this paper
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