The first PBC continuum extrapolation of the ΔI=1/2 K→ππ amplitude gives Re(ε'/ε)=17.5(6.8)(4.9)(5.0)×10^{-4}, consistent with the experimental 16.6(2.3).
$\pi-\pi$ scattering, QED and finite-volume quantization
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Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $\pi^+\pi^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. This is the first step in developing a complete lattice QCD calculation of the electromagnetic and isospin-breaking light-quark mass contributions to $\varepsilon'$, the parameter describing direct CP violating effects in $K_L\to\pi\pi$ decay.
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$\Delta I =1/2$ process of $K\to\pi\pi$ decay on multiple ensembles with periodic boundary conditions
The first PBC continuum extrapolation of the ΔI=1/2 K→ππ amplitude gives Re(ε'/ε)=17.5(6.8)(4.9)(5.0)×10^{-4}, consistent with the experimental 16.6(2.3).