High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks

Abstract

We determine the non-perturbatively renormalized axial current for O($a$) improved lattice QCD with Wilson quarks. Our strategy is based on the chirally rotated Schrödinger functional and can be generalized to other finite (ratios of) renormalization constants which are traditionally obtained by imposing continuum chiral Ward identities as normalization conditions. Compared to the latter we achieve an error reduction up to one order of magnitude. Our results have already enabled the setting of the scale for the $N_{\mathrm{f}}=2+1$ CLS ensembles [1] and are thus an essential ingredient for the recent ${\alpha }_s$ determination by the ALPHA collaboration [2]. In this paper we shortly review the strategy and present our results for both $N_{\mathrm{f}}=2$ and $N_{\mathrm{f}}=3$ lattice QCD, where we match the $\beta$-values of the CLS gauge configurations. In addition to the axial current renormalization, we also present precise results for the renormalized local vector current.

arXiv comment43 pages, 11 figures. Added Appendix C containing fits to the final results for Z_{A,V}. Matches published version

References in corpus (44)

• Properties and uses of the Wilson flow in lattice QCD
• Chiral symmetry and O(a) improvement in lattice QCD
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Ab initio calculation of the neutron-proton mass difference
• Chirally improving Wilson fermions - I. O(a) improvement
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Non-perturbative determination of the axial current normalization constant in O(a) improved lattice QCD
• On the Schroedinger functional in QCD
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Lattice QCD with open boundary conditions and twisted-mass reweighting
• The strange quark mass and Lambda parameter of two flavor QCD
• O(a) improvement of the axial current in lattice QCD to one-loop order of perturbation theory
• Further results on O(a) improved lattice QCD to one-loop order of perturbation theory
• Setting the scale for the CLS $2+1$ flavor ensembles
• Chirally improving Wilson fermions
• Physical Point Simulation in 2+1 Flavor Lattice QCD
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• The running coupling from the QCD Schrödinger functional -- a one-loop analysis
• One-loop renormalization of the QCD Schrödinger functional
• Tuning the strange quark mass in lattice simulations
• Improvement of N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• Non-perturbative renormalization of the axial current with dynamical Wilson fermions
• O(a) improved twisted mass lattice QCD
• Automatic differentiation for error analysis of Monte Carlo data
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Perturbative Renormalization Factors of Bilinear Quark Operators for Improved Gluon and Quark Actions in Lattice QCD
• Determination of the QCD $\Lambda$-parameter and the accuracy of perturbation theory at high energies
• Computation of the improvement coefficient $c_{\mathrm{sw}}$ to 1-loop with improved gluon actions
• Non-perturbative improvement of the axial current in N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• On cutoff effects in lattice QCD from short to long distances
• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Step scaling and the Yang-Mills gradient flow
• The three-loop beta-fuction of QCD with the clover action
• Lattice QCD with a chiral twist
• A non-perturbative exploration of the high energy regime in $N_{\text{f}}=3$ QCD
• Perturbative renormalization of bilinear quark and gluon operators
• A perturbative determination of O(a) boundary improvement coefficients for the Schrödinger Functional coupling at 1-loop with improved gauge actions
• Mass-improvement of the vector current in three-flavor QCD
• Critical slowing down and the gradient flow coupling in the Schrödinger functional
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: applications
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: non-perturbative tuning
• The chirally rotated Schrödinger functional: theoretical expectations and perturbative tests
• Testing universality and automatic O(a) improvement in massless lattice QCD with Wilson quarks

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