Non-perturbative renormalisation and improvement of non-singlet tensor currents in $N_\mathrm{f}=3$ QCD

TL;DR

This paper non-perturbatively determines the renormalisation of non-singlet tensor currents in three-flavor QCD, eliminating perturbative uncertainties and providing precise renormalisation factors for lattice QCD calculations.

Contribution

It introduces a recursive finite-size scaling method to fully resolve the RG running of tensor currents and provides the first non-perturbative determination of the Symanzik counterterm c_T.

Findings

Total renormalisation factor at 233 MeV scale provided.

First non-perturbative determination of c_T from an axial Ward identity.

Elimination of perturbative RG ambiguities in tensor current renormalisation.

Abstract

Hadronic matrix elements involving tensor currents play an important r\^ole in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schr\"odinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm $c_\mathrm{T}$ derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.