Abstract
We analyse for the first time the CP violating ratio ε′/ε in K → ππ decays in leptoquark (LQ) models. Assuming a mass gap to the electroweak (EW) scale, the main mechanism for LQs to contribute to ε′/ε is EW gauge-mixing of semi-leptonic into non-leptonic operators, which we treat in the Standard Model effective theory (SMEFT). We perform also the one-loop decoupling for scalar LQs, finding that in all models with both left-handed and right-handed LQ couplings box-diagrams generate numerically strongly enhanced EW-penguin operators Q8,8′ already at the LQ scale. We then investigate correlations of ε′/ε with rare Kaon processes (\( {K}_L\to {\pi}^0\nu \overline{\nu} \), \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \), \( {K}_L\to {\pi}^0\ell \overline{\ell} \), \( {K}_S\to \mu \overline{\mu} \), ΔM K and ε K ) and find that even imposing only a moderate enhancement of (ε′/ε)NP = 5 × 10−4 to explain the current anomaly hinted by the Dual QCD approach and RBC-UKQCD lattice QCD calculations leads to conflicts with experimental upper bounds on rare Kaon processes. They exclude all LQ models with only a single coupling as an explanation of the ε′/ε anomaly and put strong-to-serious constraints on parameter spaces of the remaining models. Future results on \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) from the NA62 collaboration, \( {K}_L\to {\pi}^0\nu \overline{\nu} \) from the KOTO experiment and \( {K}_S\to \mu \overline{\mu} \) from LHCb will even stronger exhibit the difficulty of LQ models in explaining the measured ε′/ε, in case the ε′/ε anomaly will be confirmed by improved lattice QCD calculations. Hopefully also improved measurements of \( {K}_L\to {\pi}^0\ell \overline{\ell} \) decays will one day help in this context.
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Bobeth, C., Buras, A.J. Leptoquarks meet ε′/ε and rare Kaon processes. J. High Energ. Phys. 2018, 101 (2018). https://doi.org/10.1007/JHEP02(2018)101
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DOI: https://doi.org/10.1007/JHEP02(2018)101