Nonperturbative renormalization and running of composite operators in the Schrodinger Functional scheme

In asymptotic free theories QCD-like, the perturbative computation of the RG evolution is limited to a short range scales at high energies. In this talk I will present some recent (preliminary) results for the non-perturbative first-principle computation of the renormalization and running of the tensor currents ($N_f=0,2$) and the BSM four-fermion operators $\Delta F=2 (N_f=2)$, and of quark masses ($N_f=3$). Thanks to the recursive finite-size scaling techniques in the Schrödinger Functional (SF) renormalization scheme , developed by the ALPHA collaboration, it is possible to provide the non-perturbative running over two orders of magnitude in scales, from low energies $O(\Lambda_{QCD})$ to high energies $O(M_W)$ where perturbation theory can be safely applied.

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