Note on Rome-Southampton renormalization with smeared gauge fields

Abstract

We have calculated continuum limit step scaling functions of bilinear and four-fermion operators renormalized in a Rome-Southampton scheme using various smearing prescriptions for the gauge field. Also, for the first time, we have calculated non-perturbative anomalous dimensions of operators renormalized in a Rome-Southampton scheme. The effect of such smearing first enters connected fermionic correlation functions via radiative corrections. We use off-shell renormalisation as a probe, and observe that the upper edge of the Rome-Southampton window is reduced by link smearing. This can be interpreted as arising due to the fermions decoupling from the high momentum gluons and we observe that the running of operators with the scale at large lattice momenta shows enhanced lattice artefacts. We find that the effect is greater for HEX smearing than for Stout smearing, but that in both cases additional care must be taken when using off-shell renormalisation with smeared gauge fields compared to thin link simulations.

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

“…This reduced upper edge of the renormalization window may be from the usage of link smearing as discussed in Ref. [27]. We are interested in checking this on thin link configurations in the future.…”

“…In Ref. [27] the upper edge of the renormalization window was found to be reduced by link smearing. We may do a calculation on thin link configurations to check this in the future.…”

Nucleon charges and electromagnetic form factors from2+1+1-flavor lattice QCD

“…We observe this improvement in the calculations of two and three-point correlation functions. HYP smearing also modifies the discretization artifacts appearing at high momentum in the calculation of the renormalization constants [26]. We describe our strategy for estimating the associated systematic uncertainty in Sec.…”

“…Recent analyses have shown that smeared lattices alter the window in which lattice data are consistent with perturbation theory [26]. HYP smearing smooths the gauge fields in a 2 4 hypercube, so gluons with momentum of order 1/a are suppressed, modifying the high-q 2 behavior of Z Γ .…”

“…The error on this estimate is taken to be half of the total variation in the range 4 < q 2 < 6 GeV 2 . In the second case we assume an ansatz for the lattice artifacts and fit the q 2 dependence of the data [26]. We try several variations of c/q 2 + Z + d 1 q + d 2 q 2 and of the fit range.…”