An obvious isospin breaking correction to epsilon' of kinematical origin

Abstract

Isospin breaking correction to the $ΔI = {1/2}$ decay of $K\toππ$ generates a large enough contribution to $ε'$ through an induced $ΔI = {3/2}$ amplitude in $K_L$ decay. Aside from the $π$-$η$ and $π$-$η'$ mixing contributions, there is a correction of kinematical origin due to the final-state $π^{\pm}$-$π^0$ mass difference, which is unambiguously calculable from the low-energy off-shell behavior of the $K\toππ$ amplitude. This correction to $ε'$ reduces the isospin breaking parameter $Ω_{IB}$ by 0.06, which is nearly one half of the $π$-$η$ mixing effect computed with chiral Lagrangians to $O(p^2)$.