An obvious isospin breaking correction to epsilon' of kinematical origin

Details An obvious isospin breaking correction to epsilon' of kinematical origin An obvious isospin breaking correction to epsilon' of kinematical origin

2001-02-08

arxiv.org/abs/hep-ph/0102108v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

3 pages with no figure in REVTEX

Scientific paper

Isospin breaking correction to the $\Delta I = {1/2}$ decay of $K\to\pi\pi$ generates a large enough contribution to $\epsilon'$ through an induced $\Delta I = {3/2}$ amplitude in $K_L$ decay. Aside from the $\pi$-$\eta$ and $\pi$-$\eta'$ 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 $\epsilon'$ 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 $O(p^2)$.

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