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

TL;DR

This paper presents the first direct calculation of on-shell $K o ext{pi} ext{pi}$ hadronic matrix elements of chromomagnetic operators using Dual QCD, providing insights relevant for new physics and the $ ext{epsilon}^ ext{prime}/ ext{epsilon}$ anomaly.

Contribution

It introduces a novel direct calculation of chromomagnetic operator matrix elements in the Standard Model and beyond using Dual QCD, including off-shell $K- ext{pi}$ matrix elements for comparison with lattice QCD.

Findings

Single $B$ parameter $B_{ m CMO}=0.33$ in the SU(3) chiral limit

Small corrections beyond the chiral limit are expected based on ETM collaboration results

Results are relevant for understanding the $ ext{epsilon}^ ext{prime}/ ext{epsilon}$ anomaly in new physics scenarios

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 $B_{\rm CMO}=0.33$. 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.