Abstract
The Standard Model (SM) prediction for the ratio ε′/ε appears to be significantly below the experimental data. Also ε K in the SM tends to be below the data. Any new physics (NP) removing these anomalies will first of all have impact on flavour observables in the K meson system, in particular on rare decays K + → π + ν ν ¯ $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ , K L → π 0 ν ν ¯ $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ , K L → μ + μ − and K L → π 0 ℓ + ℓ − and ΔM K . Restricting the operators contributing to ε′/ε to the SM ones and to the corresponding primed operators, NP contributions to ε′/ε are quite generally dominated either by QCD penguin (QCDP) operators Q 6(Q 6 ′ ) or electroweak penguin (EWP) operators Q 8(Q 8 ′ ) with rather different implications for other flavour observables. Our presentation includes general models with tree-level Z and Z′ flavour violating exchanges for which we summarize known results and add several new ones. We also briefly discuss few specific models. The correlations of ε′/ε with other flavour observables listed above allow to differentiate between models in which ε′/ε can be enhanced. Various DNA-tables are helpful in this respect. We find that simultaneous enhancements of ε′/ε, ε K , ℬ K L → π 0 ν ν ¯ $$ \mathrm{\mathcal{B}}\left({K}_L\to {\pi}^0\nu \overline{\nu}\right) $$ and ℬ K + → π + ν ν ¯ $$ \mathrm{\mathcal{B}}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right) $$ in Z scenarios are only possible in the presence of both left-handed and right-handed flavour-violating couplings. In Z′ scenarios this is not required but the size of NP effects and the correlation between ℬ K L → π 0 ν ν ¯ $$ \mathrm{\mathcal{B}}\left({K}_L\to {\pi}^0\nu \overline{\nu}\right) $$ and ℬ K + → π + ν ν ¯ $$ \mathrm{\mathcal{B}}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right) $$ depends strongly on whether QCDP or EWP dominate NP contributions to ε′/ε. In the QCDP case possible enhancements of both branching ratios are much larger than for EWP scenario and take place only on the branch parallel to the Grossman-Nir bound, which is in the case of EWP dominance only possible in the absence of NP in ε K .We point out that QCDP and EWP scenarios of NP in ε′/ε can also be uniquely distinguished by the size and the sign of NP contribution to ΔM K , elevating the importance of the precise calculation of ΔM K in the SM. We emphasize the importance of the theoretical improvements not only on ε′/ε, ε K and ΔM K but also on K L → μ + μ −, K L → π 0 ℓ + ℓ −, and the K → ππ isospin amplitudes ReA 0 and ReA 2 which would in the future enrich our analysis.