I report on the application of tmQCD techniques to the computation of hadronic matrix elements of four-fermion operators. Emphasis is put on the computation of $B_K$ in quenched QCD performed by the ALPHA Collaboration. The extension of tmQCD strategies to the study of neutral $B$-meson mixing is briefly discussed. Finally, some remarks are made concerning proposals to apply tmQCD to the computation of $K\to\pi\pi$ amplitudes.
Categories: hep-lat