Volume 518 - The 42nd International Symposium on Lattice Field Theory (LATTICE2025) - Parallel Session Standard Model parameters
RG running and mixing for $\Delta$F = 2 Four-Fermion Operators from Step-Scaling Matrices in $\chi$SF schemes
R. Marinelli*, I. Campos Plasencia, M. Dalla Brida, G.M. de Divitiis, A. Lytle, M. Papinutto and A. Vladikas
*: corresponding author
Full text: Not available
Abstract
show preliminary results for the nonperturbative Renormalization Group (RG) running of the full $\Delta F = 2$ four-fermion operators basis in QCD with $N_f = 3$ massless dynamical flavors. The perturbative part of the running is obtained extending the conventional approaches in the literature, employing the Poincaré–Dulac theorem. The nonperturbative computations employ $\mathcal{O}(a)$-improved Wilson fermions in a mixed action framework: chirally rotated Schrödinger functional ($\chi$SF) boundary conditions for valence quarks and standard Schrödinger Functional (SF) boundaries for the sea quarks. The RG evolution operators are determined through matrix step-scaling functions (SSF), using a SF coupling in the perturbative regime down to $\sim4$ GeV, and a Gradient Flow (GF) coupling from $\sim 4$ GeV down to $\sim 200$ MeV. Moreover, the results have been obtained in two different normalization schemes and validated through a variety of consistency checks
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