$B_K$ and Explicit Chiral Symmetry Breaking

The $B_K$ parameter is discussed in the general context of calculating beyond the factorization approximation for hadronic matrix elements. A variant of the $1/N_c$ method of Bardeen et al. is used. We present calculations within a low energy approach and a calculation within the Nambu--Jona-Lasinio model. Matching with the QCD behaviour and dependence on non-zero current quark masses is studied.