RG-running of the tensor currents for $N_f$ =3 QCD in a $\ddot{I}‡SF$ setup

Abstract

We present the preliminary results of the non-perturbative running of the flavour non-singlet tensor operator in the high-energy range $2\mathrm{GeV}\lesssim \hat{\mathrm{I}}¼\lesssim 128\mathrm{GeV}$ in $N_f=3$ 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 Schrödinger functional (SF) boundary conditions, and valence quarks with chirally rotated Schrödinger functional ($\ddot{I}‡$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 $c_T$).

10 pages, 4 figures. Presented at the 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Bonn, Germany