RG-running of the tensor currents for N_f= 3 QCD in a XSF setup

We present the preliminary results of the non-perturbative running of the flavour non-singlet tensor operator in the high-energy range 2 GeV≲μ≲128 GeV in Nf=3 massless QCD, comparing four different definitions of the renormalisation constant. We use the configuration ensembles of arXiv:1802.05243 and arXiv:1607.06423, subject to Schroedinger functional (SF) boundary conditions, and valence quarks with chirally rotated Schroedinger functional (χSF) boundary conditions. Provided that boundary counterterms have been appropriately tuned, this results in O(a) improvement of the tensor operator, without the need of a dimension-4 Symanzik counterterm (proportional to cT).