# Non-perturbative renormalization of tensor currents: strategy and results for $N_f = 0$ and $N_f = 2$ QCD

## TL;DR

This paper develops a non-perturbative lattice QCD method to determine the renormalization group running of tensor currents, providing essential data for accurate physical amplitude calculations in QCD with zero and two flavors.

## Contribution

It introduces a recursive finite-size scaling approach for non-perturbative renormalization of tensor currents in lattice QCD and supplies continuum results for $N_f=0$ and $N_f=2$ schemes.

## Key findings

- RG running results for tensor currents in $N_f=0$ and $N_f=2$ QCD
- Matching factors for bare and RG-invariant currents across lattice spacings
- A framework enabling fully non-perturbative renormalization of tensor current amplitudes

## Abstract

Tensor currents are the only quark bilinear operators lacking a non-perturbative determination of their renormalisation group (RG) running between hadronic and electroweak scales. We develop the setup to carry out the computation in lattice QCD via standard recursive finite-size scaling techniques, and provide results for the RG running of tensor currents in $N_f = 0$ and $N_f = 2$ QCD in the continuum for various Schr\"odinger Functional schemes. The matching factors between bare and renormalisation group invariant currents are also determined for a range of values of the lattice spacing relevant for large-volume simulations, thus enabling a fully non-perturbative renormalization of physical amplitudes mediated by tensor currents.