Kaon Physics Without New Physics in $\varepsilon_K$

TL;DR

This paper demonstrates that within the Standard Model, it is possible to explain kaon physics without invoking new physics in ko, by using a method that avoids tensions in CKM parameter determinations and predicts correlations among rare decay observables.

Contribution

It introduces a novel approach to determine CKM parameters without assuming new physics in ko, providing precise SM predictions and analyzing implications within Z' models.

Findings

CKM parameters can be determined without NP assumptions.

SM predictions for rare K and B decays are highly accurate.

Correlations between kaon decay observables are established.

Abstract

Despite the observation of significant suppression of $b\to s\mu^+\mu^-$ branching ratios no clear sign of New Physics (NP) has been identified in $\Delta F=2$ observables, in particular to $\varepsilon_K$. Assuming negligible NP contributions to these observables allows us to determine CKM parameters without being involved in the tensions between inclusive and exclusive determinations of $V_{cb}$ and $V_{ub}$. Furthermore, this method avoids the impact of NP on the determination of these parameters present likely in global fits. Simultaneously it provides SM predictions for numerous rare $K$ and $B$ branching ratios that are most accurate to date. Analyzing this scenario within $Z^\prime$ models we point out, following the 2009 observations of Monika Blanke and ours of 2020, that despite the absence of NP contributions to $\varepsilon_K$, significant NP contributions to several rare Kaon decays, $\varepsilon'/\varepsilon$ and $\Delta M_K$ can be present. In the simplest scenario, this is guaranteed by a single non-vanishing imaginary left-handed $Z^\prime$ coupling $g^L_{sd}$. This scenario implies very stringent correlations between the Kaon observables considered by us. In particular, the identification of NP in any of these observables implies automatically NP contributions to the remaining ones. A characteristic feature of this scenario is a strict correlation between $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ branching ratios on a branch parallel to the Grossman-Nir bound. Moreover, $\Delta M_K$ is automatically suppressed as seems to be required by recent lattice QCD results.