Reply to “Comment on ‘Lattice gluon and ghost propagators and the strong coupling in pure $SU(3)$ Yang-Mills theory: Finite lattice spacing and volume effects’ ”

The quenched gluon and ghost propagator data published in [Duarte et al. Phys. Rev. D 94, 014502 (2016).] is reanalyzed following the suggestion of [Boucaud et al. Phys. Rev. D 96, 098501 (2017).] to resolve the differences between the infrared data of the simulations. Our results confirm that the procedure works well either for the gluon or for the ghost propagator but not for both propagators simultaneously as the observed deviations in the data follow opposite patterns. Definitive conclusions require improving the determination of the (ratios) of lattice spacings. A simple procedure for the relative calibration of the lattice spacing in lattice simulations is suggested.

Figure 1

Renormalized gluon propagator (top) and ghost dressing function (bottom).

Figure 2

“Recalibrated” gluon propagator: (top) $44^4$ and $\beta =5.7$ data for momenta below 1 GeV; (middle) above 1 GeV; (bottom) $128^4$ and $\beta =6.3$ data for momenta below 1 GeV.

Figure 3

Recalibrated gluon dressing function.

Figure 4

Recalibrated ghost propagator data: (top) $44^4$ and $\beta =5.7$ for momenta below 1 GeV; (bottom) above 1 GeV.