An obvious isospin breaking correction to epsilon' of kinematical origin

Abstract

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

Comments: 3 pages with no figure in REVTEX