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We present our strategy and some preliminary results for the renormalizationof four-quark operators relevant for kaon physics. We follow thenon-perturbative Rome-Southampton method, with both exceptional andnon-exceptional kinematics. We also implement momentum sources and twistedboundary conditions. We use an (almost) unitary setup: Domain-Wall valence onnf=2+1 Domain-Wall sea and Iwasaki gauge action, at two values of the latticespacing corresponding to approximately 0.086 fm and 0.114 fm . The chiralproperties of these fermions play a crucial role in this compuation and arestudied in detail in this work.

Non-perturbative renormalization of kaon four-quark operators with nf=2+1 Domain Wall fermions