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The measurements of $V_{us}$ in leptonic $(K_{\mu 2})$ and semileptonic$(K_{l3})$ kaon decays exhibit a $3\sigma$ disagreement, which could originateeither from physics beyond the Standard Model or some large unidentifiedStandard Model systematic effects. Clarifying this issue requires a carefulexamination of all existing Standard Model inputs. Making use of anewly-proposed computational framework and the most recent lattice QCD results,we perform a comprehensive re-analysis of the electroweak radiative correctionsto the $K_{e3}$ decay rates that achieves an unprecedented level of precisionof $10^{-4}$, which improves the current best results by almost an order ofmagnitude. No large systematic effects are found, which suggests that theelectroweak radiative corrections should be removed from the ``list ofculprits'' responsible for the $K_{\mu 2}$--$K_{l3}$ discrepancy.

Improved $K_{e3}$ radiative corrections sharpen the $K_{\mu 2}$--$K_{l3}$ discrepancy