Delta M_K and epsilon_K in SUSY at the Next-to-Leading order

We perform a Next-to-Leading order analysis of Delta S=2 processes beyond the Standard Model. Combining the recently computed NLO anomalous dimensions and the B parameters of the most general Delta S=2 effective Hamiltonian, we give an analytic formula for Delta M_K and epsilon_K in terms of the Wilson coefficients at the high energy scale. This expression can be used for any extension of the Standard Model with new heavy particles. Using this result, we consider gluino-mediated contributions to Delta S=2 transitions in general SUSY models and provide an improved analysis of the constraints on off-diagonal mass terms between the first two generations of down-type squarks. Finally, we improve the constraints on R-violating couplings from Delta M_K and epsilon_K.