Isospin breaking in $K \rightarrow \pi\pi$ decays

Abstract

We perform a complete analysis of isospin breaking in K -> Pi Pi amplitudes in chiral perturbation theory, including both strong isospin violation and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N_c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g_8 and g_27 from a fit to K -> Pi Pi branching ratios, finding small deviations from the isospin-limit case. The ratio Re(A_0)/Re(A_2) measuring the Delta I=1/2 enhancement is found to decrese from 22.1 +/- 0.1 in the isospin limit to 20.3 +/- 0.5 in the presence of isospin breaking. We also analyse the effect of isospin violation on the CP violation parameter epsilon-prime, finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for epsilon-prime is below 15%.