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 $R_{K\pi }^{\ell =\mu ,e}=\Gamma (K\to \ell \nu )/\Gamma (\pi \to \ell \nu )$, for which many experimental uncertainties cancel, as well as the double ratio $R_{K\pi }^e/R_{K\pi }^{\mu }$, 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 $10^{-4}$ 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.

Comments: 42 pages, 18 figures. Comments are welcome