On epsilon_K 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 K0 -- K0bar 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 kappa_epsilon = 0.94 +/- 0.02.