Non-perturbative renormalization of tensor bilinears in Schr\"odinger Functional schemes

TL;DR

This paper investigates the non-perturbative renormalization group evolution of tensor bilinears in Schr"odinger Functional schemes for QCD with different flavors, providing both perturbative and non-perturbative results.

Contribution

It introduces a non-perturbative approach to renormalize tensor bilinears in SF schemes, including calculations of anomalous dimensions and discretization effects for various lattice actions.

Findings

Non-perturbative running over two orders of magnitude in energy scales.

Calculation of two-loop anomalous dimensions for tensor currents.

Discretization effects characterized for Wilson and improved actions.

Abstract

We present preliminary result for the study of the renormalization group evolution of tensor bilinears in Schr\"odinger Functional (SF) schemes for $N_f=0$ and $N_f=2$ QCD with non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions. First $N_f=2+1$ results (proceeding in parallel with the ongoing computation of the running quark masses [1] are also discussed. A one-loop perturbative calculation of the discretisation effects for the relevant step scaling functions has been carried out for both Wilson and $\mathcal{O}(a)$-improved actions and for a large number of lattice resolutions. We also calculate the two-loop anomalous dimension in SF schemes for tensor currents through a scheme matching procedure with RI and $\overline{\rm MS}$. Thanks to the SF iterative procedure the non-perturbative running over two orders of magnitude in energy scales, as well as the corresponding Renormalization Group Invariant operators, have been determined.