RG-running of the tensor currents for $N_f$ =3 QCD in a $\chi SF$ setup

TL;DR

This paper reports on the non-perturbative study of the tensor operator running in Nf=3 QCD using a chiSF setup, comparing different renormalization schemes in the high-energy regime.

Contribution

It introduces a novel non-perturbative approach to compute tensor operator running in Nf=3 QCD with chiSF boundary conditions, achieving O(a) improvement without additional counterterms.

Findings

Consistent tensor running results across four renormalization schemes.

Effective O(a) improvement without dimension-4 counterterms.

Running results applicable in the 2-128 GeV energy range.

Abstract

We present the preliminary results of the non-perturbative running of the flavour non-singlet tensor operator in the high-energy range $2~\rm{GeV}\lesssim \mu\lesssim 128~\rm{GeV}$ 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 Schr\"odinger functional (SF) boundary conditions, and valence quarks with chirally rotated Schr\"odinger functional ($\chi$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 $c_T$).