Abstract
We determine the non-perturbatively renormalized axial current for hbox {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 by 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 (Bruno et al. in Phys Rev D 95(7):074504. arXiv:1608.08900, 2017) and are thus an essential ingredient for the recent alpha _s determination by the ALPHA collaboration (Phys Rev Lett 119(10):102001. arXiv:1706.03821, 2017). 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.
Highlights
Lattice regularizations with Wilson type fermions [3] are widely used in current lattice QCD simulations [4,5,6,7,8,9,10]
We just note that with our statistics and our rather conservative approach, the propagated uncertainties are typically larger than the statistical errors for the R-estimators Eqs. (2.15), (2.17)
Our estimates for the systematic uncertainties due to deviations from the chosen line of constant physics” (LCP) were obtained analogously to the case of Nf = 2; we refer the reader to Appendix B for the details
Summary
Lattice regularizations with Wilson type fermions [3] are widely used in current lattice QCD simulations [4,5,6,7,8,9,10]. Wilson fermions maintain the full flavour symmetry of the continuum action, as well as the discrete symmetries such as parity, charge conjugation and time reversal. The matrix elements of the axial Noether currents between pion or kaon states and the vacuum, parametrized by the decay constants fπ,K , e.g. can be related to the measured life times of pions and kaons. The main strategy consists in imposing continuum chiral symmetry relations as normalization conditions at finite lattice spacing [11,12]. This is usually done using chiral Ward identities, which follow from an infinitesimal chiral change of variables in the QCD path integral.
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