$K\to \pi \pi$ and $K-\pi$ Matrix Elements of the Chromomagnetic Operators from Dual QCD

Abstract

We perform for the first time a direct calculation of on-shell $K\to \pi \pi$ hadronic matrix elements of chromomagnetic operators (CMO) in the Standard Model and beyond. To his end, we use the successful Dual QCD (DQCD) approach in which we also consider off-shell $K-\pi$ matrix elements that allows the comparison with lattice QCD calculations of these matrix elements presented recently by the ETM collaboration. Working in the SU(3) chiral limit, we find for the single $B$ parameter $B_{\mathrm{CMO}}=0.33$. Using the numerical results provided by the ETM collaboration we argue that only small corrections beyond that limit are to be expected. Our results are relevant for new physics scenarios in the context of the emerging ${\epsilon }^{\prime }/\epsilon$ anomaly strongly indicated within DQCD and supported by RBC-UKQCD lattice collaboration.

14 pages, no figures, clarifications in Section 5.3 added, conclusions unchanged

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• $K\to \pi$ matrix elements of the chromomagnetic operator on the lattice
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• The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ in the SM: 2019