Another SMEFT Story: $Z^\prime$ Facing New Results on $\varepsilon'/\varepsilon$, $\Delta M_K$ and $K\to\pi\nu\bar\nu$

TL;DR

This paper explores how a $Z'$ boson within SMEFT can explain recent anomalies in kaon decays and mixing, highlighting the role of electroweak penguins and CP-violating phases in accommodating new physics effects.

Contribution

It provides a comprehensive analysis of $Z'$-mediated new physics effects on kaon observables within SMEFT, including the impact of top Yukawa RG effects on FCNCs and constraints from recent lattice results.

Findings

NP can enhance or suppress $ ext{ε'/ε}$ within current bounds.

Suppression of $ ext{Δ}M_K$ requires new CP-violating phases.

Heavy $Z'$ can induce FCNCs via top Yukawa RG effects.

Abstract

Recently the RBC-UKQCD lattice collaboration presented new results for the hadronic matrix elements relevant for the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM). With the present knowledge of the Wilson coefficients and isospin breaking effects there is still much room for new physics (NP) contributions to $\varepsilon'/\varepsilon$ which could both enhance or suppress this ratio to agree with the data. The new SM value for the $K^0-\bar K^0$ mass difference $\Delta M_K$ from RBC-UKQCD is on the other hand by $2\sigma$ above the data hinting for NP required to suppress $\Delta M_K$. Simultaneously the most recent results for $K^+\rightarrow\pi^+\nu\bar\nu$ from NA62 and for $K_{L}\rightarrow\pi^0\nu\bar\nu$ from KOTO still allow for significant NP contributions. We point out that the suppression of $\Delta M_K$ by NP requires the presence of new CP-violating phases with interesting implications for $K\to\pi\nu\bar\nu$, $K_S\to\mu^+\mu^-$ and $K_L\to\pi^0\ell^+\ell^-$ decays. Considering a $Z^\prime$-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on $\varepsilon'/\varepsilon$. The NP QCD penguin scenario for $\varepsilon'/\varepsilon$ is excluded by SMEFT renormalization group effects in $\varepsilon_K$ so that NP effects in $\varepsilon'/\varepsilon$ are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy $Z^\prime$ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM $Z$-boson. The outcome turns out to be very interesting.