Non-perturbative renormalization of tensor currents: strategy and results for $$N_f=0$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>0</mn></mrow></math> and $$N_f=2$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn></mrow></math> QCD

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 $$N_f=0$$ Nf=0 and $$N_f=2$$ Nf=2 QCD in the continuum for various Schr&#246;dinger 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.