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

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 L\"uscher-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.