RG running from Step-Scaling Matrices in χ SF schemes for ΔF = 2 Four-Fermion Operators

We present preliminary results for the Renormalization Group (RG) running of the complete basis of ΔF=2 four-fermion operators in QCD with Nf=3 dynamical massless flavours. We use O(a)-improved Wilson fermions in a mixed action setup, with chirally rotated Schrödinger functional (χ SF) boundary conditions for the valence quarks and Schrödinger functional (SF) boundary conditions for the sea quarks. The RG evolution operators are evaluated non-perturbatively via the matrix step-scaling functions (matrix SSF) using a SF coupling from the perturbative region down to ∼4 GeV and a Gradient Flow (GF) coupling from ∼4 GeV down to ∼250 MeV. The perturbative running is computed through a novel approach that extends the usual computations in the literature relying on consequences of the Poincaré-Dulac theorem.