Long-distance contributions to kaon decays on the lattice
En-Hung Chao
TL;DR
This work surveys how lattice QCD tackles long-distance effects and QED corrections in kaon decays, focusing on frameworks that use bi-local operators and regulator schemes to connect lattice results with continuum Wilson coefficients. It highlights practical implementations for $K^+\to\pi^+\nu\bar{\nu}$, $K^+\to\pi^+\ell^+\ell^-$, and $K_L\to\mu^+\mu^-$, including IR regulation, finite-volume control, and variance-reduction strategies, with initial numerical results indicating feasibility and controlled systematic uncertainties. The contributions underscore progress in precise SM predictions for kaon processes and pave the way for robust constraints on New Physics from low-energy measurements. Overall, these advances enhance nonperturbative control of long-distance amplitudes and radiative corrections, enabling more reliable tests of the SM through kaon decays.
Abstract
In the past decades, significant improvements have been made on standard-model predictions on kaon decays using lattice quantum chromodynamics. In these proceedings, I review selected works on long-distance contributions to kaon decays and developments on QED corrections to those.