Leptoquarks meet ε ′/ ε and rare Kaon processes

摘要

A bstract 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 Q ~(8,8)′ already at the LQ scale. We then investigate correlations of ε _(′) /ε with rare Kaon processes ( K L → π 0 ν ν ˉ $$ {K}_Lo {pi}^0u overline{u} $$ , K + → π + ν ν ˉ $$ {K}^{+}o {pi}^{+}u overline{u} $$ , K L → π 0 ? ? ˉ $$ {K}_Lo {pi}^0ell overline{ell} $$ , K S → μ μ ˉ $$ {K}_So mu overline{mu} $$ , Δ M ~( 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 + → π + ν ν ˉ $$ {K}^{+}o {pi}^{+}u overline{u} $$ from the NA62 collaboration, K L → π 0 ν ν ˉ $$ {K}_Lo {pi}^0u overline{u} $$ from the KOTO experiment and K S → μ μ ˉ $$ {K}_So mu overline{mu} $$ 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 → π 0 ? ? ˉ $$ {K}_Lo {pi}^0ell overline{ell} $$ decays will one day help in this context.