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.

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

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• Ab initio calculation of the neutron-proton mass difference
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• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Step scaling and the Yang-Mills gradient flow
• A non-perturbative exploration of the high energy regime in $N_{\text{f}}=3$ QCD
• Mass-improvement of the vector current in three-flavor QCD
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• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
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• Mass-improvement of the vector current in three-flavor QCD
• Determination of the charm quark mass in lattice QCD with $2+1$ flavours on fine lattices
• Non-perturbative determination of improvement coefficients b_m and b_A-b_P and normalisation factor Z_m*Z_P/Z_A with N_f=3 Wilson fermions
• How much do charm sea quarks affect the charmonium spectrum?
• Multi-level Monte Carlo computation of the hadronic vacuum polarization contribution to $(g_{\mu }-2)$
• The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks
• Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $N_{\mathrm{f}}=3$ QCD with Wilson quarks
• Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\mathrm{g}}$
• A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Aspects of chiral symmetry in QCD at T = 128 MeV
• Dynamical solution of the strong CP problem within QCD ?
• Non-perturbative renormalization of the QCD flavour-singlet local vector current
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• Charm sea effects on charmonium decay constants and heavy meson masses
• Towards the determination of the charm quark mass on $N_{\mathrm{f}}=2+1$ CLS ensembles
• The isoscalar octet axial form factor of the nucleon from lattice QCD
• Photon emissivity of the quark-gluon plasma: a lattice QCD analysis of the transverse channel
• Light and strange quark masses from $N_f=2+1$ simulations with Wilson fermions
• Extraction of $B_s\to D_s^{(\ast )}$ form factors from $N_f=2$ lattice QCD