ε′/ε at O(p4) in the Chiral Expansion

Abstract

After updating the determination of the combination of Kobayashi-Maskawa elements IVtdV∗ts according to our new estimate of the parameter B^K, we study the CP-violating ratio ϵ′/ϵ by means of hadronic matrix elements computed to O(p4) in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some O(p2) terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio ϵ′/ϵ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find ϵ′/ϵ=1.7+1.4−1.0×10−3. Values positive and of the order of 10−3 are therefore preferred.