A new estimate of ε′/ε Original Research Article

We discuss direct CP violation in the standard model by giving a new estimate of ε′/ε in kaon decays. Our analysis is based on the evaluation of the hadronic matrix elements of the ΔS = 1 effective quark Lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. Our estimate is fully consistent with the ΔI = 12 selection rule in K → ππ decays which is well reproduced within the same framework. By varying all parameters in the allowed ranges and, in particular, taking the quark condensate — which is the major source of uncertainty — between (−200 MeV)3 and (−280 MeV)3 we find −5.0 × 10−3 < ε′/ε < 1.4 × 10−3. Assuming for the quark condensate the improved PCAC result 〈q−q〉 = −(221 ± 17 MeV)3 and fixing ΛQCD(4) to its central value, we find the more restrictive prediction ε′/g3 = (4 ± 5) × 10−4, where the central value is defined as the average over the allowed values of Im λt in the first and second quadrants. In these estimates the relevant mixing parameter Im λt is self-consistently obtained from ε and we take mtpole = 180 ± 12 GeV. Our result is, to a very good approximation, renormalization-scale and γ5-scheme independent.