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

TL;DR

This paper non-perturbatively determines the renormalized axial and vector currents in lattice QCD with Wilson quarks, achieving significant error reduction and enabling precise scale setting and strong coupling constant determinations.

Contribution

It introduces a chirally rotated Schrödinger functional method for high-precision renormalization of currents in lattice QCD, improving accuracy over traditional Ward identity approaches.

Findings

Error reduction up to one order of magnitude in renormalization constants

Results applicable to Nf=2 and Nf=3 lattice QCD

Enabled precise scale setting and alpha_s determination

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 Schr\"odinger 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 $N_{\rm f}=2+1$ 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 $N_{\rm f}=2$ and $N_{\rm f}=3$ 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.