Non-singlet vector current in lattice QCD: $\mathrm{O}(a)$-improvement from large volumes

TL;DR

This work addresses the precise non-perturbative determination of mass-independent improvement coefficients for the non-singlet vector current in $N_\mathrm{f}=3$ Wilson fermions, a key input for accurate vector-current observables in lattice QCD. The authors employ massive axial Ward identities to extract $c_\mathrm{V}$ and $c_{\tilde{\mathrm{V}}}$ while incorporating a newly estimated mass-dependent input $\bar{b}_{\mathrm{A}}^{\mathrm{eff}}$, and validate the results across two lattice spacings and a different chiral trajectory on CLS large-volume ensembles. The updated $\bar{b}_{\mathrm{A}}^{\mathrm{eff}}$ reduces mass-dependent contamination, leading to consistent $c_\mathrm{V}$ and $c_{\tilde{\mathrm{V}}}$ between discretizations and with small-volume massless determinations, and the authors provide a global parameterization of the coefficients over the studied range of $g_0^2$. This work enhances the reliability of lattice calculations involving vector currents and supports precise SM tests by delivering improved, cross-validated improvement coefficients for both local and point-split discretizations.

Abstract

In previous work, we determined the improvement coefficients $c_\mathrm{V}$ and $c_{\tilde{\mathrm{V}}}$ required for the massless $\mathrm{O}(a)$-improvement of the local and point-split discretizations of the non-singlet vector current for $N_\mathrm{f}=3$ non-perturbatively $\mathrm{O}(a)$-improved Wilson fermions and the Lüscher-Weisz gauge action, using ensembles of large-volume configurations generated by the Coordinated Lattice Simulations (CLS) initiative. A new estimate for the mass-dependent improvement coefficient $\bar{b}_{\mathrm{A}}^\mathrm{eff}$ has recently become available, differing from the one used in our earlier study, and on which our implementation via a massive axial Ward identity relied. Here, we update our analysis of the mass-independent vector improvement coefficients based on the new axial current improvement coefficient, and analyse additional ensembles with a different chiral trajectory in order to validate our results at two values of the bare coupling. We find that using the new estimate of $\bar{b}_{\mathrm{A}}^\mathrm{eff}$ improves the consistency between the two chiral trajectories, as well as with a previous determination of the improvement coefficients directly in the massless limit on small volumes.

Figures (2)

• Figure 1: Dependence on the estimator as a function of $m^{12}$ at fixed bare coupling $\beta=6/g_0^2=3.55$ for the local (red) and point-split (blue) discretizations of the vector current. The squares display the chiral trajectory with $\bar{m}=0$ while the circles show the same with $\bar{m}=\mathrm{const.}$. The earlier results from Ref. Gerardin:2018kpy are shown in the grey triangles while the results obtained from SF Heitger:2020zaq are shown with crosses.
• Figure 2: Final results for $c_\mathrm{V}$ (red) and $c_{\tilde{\mathrm{V}}}$ (blue) as a function of the bare coupling, compared with the results of Heitger et al. Heitger:2020zaq (black line). The old results of Ref. Gerardin:2018kpy are shown with the grey triangles.