Natural complex plane for kaon CKM data: framework, status and future

Abstract

Kaon physics can be used to independently determine three out of the four parameters of the CKM matrix, without any B physics input. Treating one parameter, $|V_{us}|$, or alternatively Wolfenstein $\lambda$, as well known, we show that the natural plane for the presentation of kaon CKM information is spanned by the combinations $\left(A^2(1-\hat\rho),\, A^2 \hat\eta\right)$. In this way, the use of B physics inputs is avoided, as well as the artificial inflation of errors due to parametric uncertainties, mainly due to $|V_{cb}|$. We show that the current status of kaon CKM constraints, impacted by recent advances in measurement and theory, is characterized by four allowed regions, and find that incoming data will inevitably disfavor a number of them, either confirming the CKM paradigm as dominant, or discovering a departure from the Standard Model.