Recent calculations have pointed to a 2.8 $\sigma$ tension between data on $\epsilon^{ \prime}_K / \epsilon_K$ and the standard-model (SM) prediction. Several new physics (NP) models can explain this discrepancy, and such NP models are likely to predict deviations of $\mathcal{ B}(K\to \pi \nu \overline{ \nu})$ from the SM predictions, which can be probed precisely in the near future by NA62 and KOTO experiments. We present correlations between $\epsilon^{ \prime}_K / \epsilon_K$ and $\mathcal{ B}(K\to \pi \nu \overline{ \nu})$ in two types of NP scenarios: a box dominated scenario and a $Z$-penguin dominated one. It is shown that different correlations are predicted and the future precision measurements of $K \to \pi \nu \overline{ \nu}$ can distinguish both scenarios.
Categories: hep-ph hep-ex