Isospin-breaking contributions to ϵ ′ /ϵ

We present an updated analysis of isospin-violating corrections to ϵ0=ϵ in the framework of chiral perturbation theory, taking advantage of the currently improved knowledge on quark masses and nonperturbative parameters. The role of the different ingredients entering into the analysis is carefully assessed. Our final result is ωeff = 0:110 +0:090 -0:088 [1].