Weak vector bosons representing a compound of two Lorentz spinors may lead to CP-violating effects by a gamma-W-W interaction term. Such a term is applied to the calculation of the contribution of a particular type of graphs to the admixture parameter of the neutral K-mesons. We analyse the box graphs whose W-bosons emit a photon to the opposite quark leg in the free-quark limit. Methods of precisely calculating such two-loop graphs are presented. Novel strong-interaction matrix elements appear. It is shown that there is a CP-violating contribution. It vanishes in the mathematical quark mass limit m(s) --> m(d). We always assume that all the flavour mixing elements are real. Three main results are: 1) The experimentally observed phase arg (epsilon) of the admixture parameter can be reproduced exactly. 2) The top-quark contribution is negligible. 3) Although a logarithmical divergence appears in one of the two-loop integrals, which is regularized by the s-squark mass, the known quarks and weak bosons are not enough to reproduce the magnitude of \epsilon\. This data value would definitely point to the existence of heavy-quark partners.
