Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction

Abstract

Precision tests of first-row unitarity of the Cabibbo-Kobayashi-Maskawa matrix currently display two intriguing tensions, both at the $3\sigma$ level. First, combining determinations of $V_{ud}$ from superallowed $\beta$ decays with $V_{us}$ from kaon decays suggests a deficit in the unitarity relation. At the same time, a tension of similar significance has emerged between $K_{\ell 2}$ and $K_{\ell 3}$ decays. In this Letter, we point out that a measurement of the $K_{\mu3}/K_{\mu 2}$ branching fraction at the level of $0.2\%$ would have considerable impact on clarifying the experimental situation in the kaon sector, especially in view of tensions in the global fit to kaon data as well as the fact that the $K_{\mu2}$ channel is currently dominated by a single experiment. Such a measurement, as possible for example at NA62, would further provide important constraints on physics beyond the Standard Model, most notably on the role of right-handed vector currents.