On εK beyond lowest order in the operator product expansion

We analyse the structure of long distance (LD) contributions to the CP-violating parameter epsilon(K), that generally affect both the absorptive (Gamma(12)) and the dispersive (M-12) parts of the K-0-(K) over bar (0) mixing amplitude. We point out that, in a consistent framework, in addition to LD contributions to Im Gamma(12), estimated recently by two of us, also LD contributions to Im M-12 have to be taken into account. Estimating the latter contributions the impact of LD effects on epsilon(K) is significantly reduced (from -6.0% to -3.6%). The overall effect of LD corrections and of the superweak phase being different from 45 degrees is summarised by the multiplicative factor K-epsilon = 0.94 +/- 0.02. (c) 2010 Elsevier B.V. All rights reserved.