Complete theory of radiative corrections to Kℓ3 decays and the Vus update

Abstract

We fill up the missing piece in our own re-analysis of the long-distance electromagnetic radiative corrections to semileptonic kaon decays by performing a rigorous study in the K → πμ+νμ(γ) channels. With appropriate experimental and lattice inputs, we achieve a precision level of 10−4 in these channels. This is comparable to our previous analysis in the K → πe+νe(γ) channels. With this new result, we present an updated global analysis to extract the Standard Model parameter |Vus| from semileptonic kaon decays. We obtain |Vus| = 0.22308(55) and 0.22356(73), using the lattice average of the K0→ π− transition form factor at Nf = 2 + 1 + 1 and Nf = 2 + 1, respectively.