RG-running of the tensor currents for $N_{f}$= 3 QCD in a $\chi$SF setup

Wepresentthepreliminaryresults of the non-perturbative running of the flavour non-singlet tensor operator in the high-energy range 2 GeV 128 GeV in Nf = 3 massless QCD, comparing four different definitions of the renormalisation constant. We use the configuration ensembles of ref.[1] and ref.[2], subject to Schrödinger functional (SF) boundary conditions, and valence quarks with chirally rotated Schrödinger functional ( SF) 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).