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

The measurements of $V_{us}$ in leptonic $(K_{\mu 2})$ and semileptonic $(K_{l3})$ kaon decays exhibit a $3\sigma$ 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 $K_{e3}$ 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 $K_{\mu 2}$--$K_{l3}$ discrepancy.