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Tensor currents are the only quark bilinear operators lacking anon-perturbative determination of their renormalisation group (RG) runningbetween hadronic and electroweak scales. We develop the setup to carry out thecomputation in lattice QCD via standard recursive finite-size scalingtechniques, 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 Functionalschemes. The matching factors between bare and renormalisation group invariantcurrents are also determined for a range of values of the lattice spacingrelevant for large-volume simulations, thus enabling a fully non-perturbativerenormalization of physical amplitudes mediated by tensor currents.

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