New measurements in leptonic kaon and pion decays: experimental and theoretical perspectives

Abstract: We study the future prospects for precision measurements of purely leptonic charged-current kaon and pion decays. In particular, we consider the single ratios $$R_{Kπ}^{\ell=μ,e} = Γ(K \to \ellν) / Γ(π\to \ellν)$$, for which many experimental uncertainties cancel, as well as the double ratio $R_{Kπ}^e / R_{Kπ}<sup>μ$, which provides a particularly sensitive probe of new physics. This study is timely in light of two converging developments. On the experimental side, a new conceptual design for a dedicated setup based on a slow-extracted proton beam and a multi-year data-taking program, is expected to achieve a precision at the $10<sup>{-4}$ level. On the theory side, recent lattice-QCD calculations have reached a comparable level of accuracy. Finally, we assess the impact of these next-generation measurements on searches for physics beyond the Standard Model and show that they can provide constraints that are either competitive with or complementary to existing bounds.