We propose a new theory framework to study the electroweak radiative corrections in K l3 decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important O(G F α) radiative corrections are described by a single tensor T µν involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the K 0 l3 channel that it suffers the least impact from the poorly-constrained low energy constants. This finding may serve as a basis for a more precise extraction of the matrix element V us in the future.

The measurements of Vus in leptonic (Kμ2) and semileptonic (Kl3) kaon decays exhibit a 3σ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the Ke3 decay rates that achieves an unprecedented level of precision of 10−4, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the “list of culprits” responsible for the Kμ2–Kl3 discrepancy.

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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.