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arXiv · 2006.01138

Another SMEFT Story: $Z^\prime$ Facing New Results on $\varepsilon'/\varepsilon$, $ΔM_K$ and $K\toπν\barν$

Jason Aebischer·Andrzej J. Buras·Jacky Kumar
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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 $ΔM_K$ from RBC-UKQCD is on the other hand by $2σ$ above the data hinting for NP required to suppress $ΔM_K$. Simultaneously the most recent results for $K^+\rightarrowπ^+ν\barν$ from NA62 and for $K_{L}\rightarrowπ^0ν\barν$ from KOTO still allow for significant NP contributions. We point out that the suppression of $ΔM_K$ by NP requires the presence of new CP-violating phases with interesting implications for $K\toπν\barν$, $K_S\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ 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.

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Jason Aebischer, Andrzej J. Buras, Jacky Kumar. 2020-06-09. Another SMEFT Story: $Z^\prime$ Facing New Results on $\varepsilon'/\varepsilon$, $ΔM_K$ and $K\toπν\barν$. https://doi.org/10.1007/jhep12(2020)097

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