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

TL;DR

This paper presents a highly precise re-analysis of electroweak radiative corrections to kaon decay rates, reducing uncertainties and clarifying the source of discrepancies in $V_{us}$ measurements, with implications for Standard Model tests.

Contribution

It introduces a new computational framework and uses recent lattice QCD results to significantly improve the precision of radiative correction calculations for kaon decays.

Findings

No large systematic effects found in radiative corrections

Electroweak corrections are unlikely to explain the $K_{ ext{mu}2}$--$K_{l3}$ discrepancy

Improved precision reduces uncertainties by nearly an order of magnitude

Abstract

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.