Master formula for $\varepsilon'/\varepsilon$ beyond the Standard Model

TL;DR

This paper introduces a comprehensive master formula for the $'/$ ratio in any BSM theory, utilizing recent hadronic matrix element calculations, highlighting the significance of scalar and tensor operators in the emerging anomaly.

Contribution

It provides the first universal master formula for $'/$ beyond the Standard Model, integrating recent theoretical calculations and implementing them in an open source code.

Findings

Scalar and tensor BSM operators significantly impact $'/$.

The master formula is applicable to any BSM theory.

Results are available in the open source code flavio.

Abstract

We present for the first time a master formula for $\varepsilon'/\varepsilon$, the ratio probing direct CP violation in $K \to \pi\pi$ decays, valid in any theory beyond the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM operators calculated recently in the Dual QCD approach and the ones of the SM operators from lattice QCD. We emphasize the large impact of several scalar and tensor BSM operators in the context of the emerging $\varepsilon'/\varepsilon$ anomaly. We have implemented the results in the open source code flavio.