Lattice-QCD prediction for electronic kaon-to-pion leptonic decay ratios

Determine a precise lattice-QCD Standard Model prediction for the electronic ratio of kaon-to-pion leptonic decay widths, $R_{K\pi}^{e}$, to replace the absence of an existing precise lattice calculation and support future-physics analyses.

Background

The paper studies the ratios $$R_{K\pi}^{\ell}=\Gamma(K^+\to\ell^+\nu)/\Gamma(\pi^+\to\ell^+\nu)$$ and emphasizes that their Standard Model interpretation depends on hadronic inputs and radiative corrections. A precise lattice-QCD determination exists for the muonic case, but the authors state that no comparably precise Standard Model prediction is currently available for the electronic ratio.

The absence of a precise electronic prediction limits the direct theoretical interpretation of future measurements of $R_{K\pi}^{e}$. In the radiative-correction discussion, the authors likewise state that a lattice determination of the electronic long-distance correction $\delta_{\rm ew}^{Pe}$ is unavailable and therefore use a chiral-perturbation-theory estimate instead.