Correlations of ${ϵ}_K^{\prime }/{ϵ}_K$ with $K\to \pi \nu \overline{\nu }$ in Models of New Physics

Abstract

Recent calculations have pointed to a 2.8 $\sigma$ tension between data on ${ϵ}_K^{\prime }/{ϵ}_K$ 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 ${ϵ}_K^{\prime }/{ϵ}_K$ 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.

Comments: 4 pages, 2 figures; Contribution to proceedings of 52th Rencontres de Moriond electroweak interactions and unified theories, La Thuile, Italy, 18-25 March, 2017; references added