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We present unquenched lattice QCD results for the matrix elements offour-fermion operators relevant to the description of the neutral K and Dmixing in the Standard Model and its extensions. We have employed simulationswith Nf = 2 + 1 + 1 dynamical sea quarks at three values of the latticespacings in the interval 0.06 - 0.09 fm and pseudoscalar meson masses in therange 210 - 450 MeV. Our results are extrapolated to the continuum limit and tothe physical pion mass. Renormalization constants have been determinednon-perturbatively in the RI-MOM scheme. In particular, for the Kaonbag-parameter, which is relevant for the \overline{K}^0-K^0 mixing in theStandard Model, we obtain B_K^{RGI} = 0.717(24).

\Delta S=2 and \Delta C=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD