SciPost Submission Page
Constraining the gauge-fixed Lagrangian in minimal Landau gauge
by Axel Maas
This is not the current version.
|As Contributors:||Axel Maas|
|Submitted by:||Maas, Axel|
|Submitted to:||SciPost Physics|
|Subject area:||High-Energy Physics - Theory|
A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.
Submission & Refereeing History
Reports on this Submission
Anonymous Report 1 on 2019-12-26 Invited Report
1- Well written
2- Problem addressed clearly stated
3- Study how to compare different non-perturbative techniques results for QCD
4- New way to address the comparison
1- Does not include a full discussion of all issues
2- Biased discussion at the end
"Constraining the gauge-fixed Lagrangian in minimal Landau gauge"
The manuscript under appreciation discuss an important issue for the non-perturbative regime of QCD, the comparison between lattice simulations and Dyson-Schwinger (DS) results. The manuscript is well written and the problem is clearly stated. After a general introduction, the author writes the generating functional for the continuum formulation of the minimal Landau gauge, that is “identified” with the continuum version of the lattice formulation, and the usual Faddeev-Popov (FP) functional. Then the FP is used to write the Dyson-Schwinger equation for the ghost propagator that involves the gluon and ghost propagators and ghost-gluon vertex. This is one of the simplest DS equations and the author uses it as a benchmark to compare lattice and DS results.
(i) Although the author provides a good discussion of various issues, he forgets to mention that on the lattice, if one excludes the corresponding perturbative treatment, there are no ghost fields and the ghost propagator is “recovered” mimicking the usual continuum procedure. To the referee this is an important point that the author should mention in Sec. 2 to alert the reader.
The results of 3D and 4D lattice simulations, for various lattice spacings and volumes, are used in the ghost DS equation to check if the equations is solved exactly. The full exercise requires the computation of the gluon and ghost propagators, together with the lattice computation of the ghost-gluon vertex that is performed for three kinematical configurations. In all the computations large statistical ensembles are used. The manuscript includes a nice discussion of the results obtained for the various Green functions and of the deviations between lattice and continuous calculations.
(ii) However, the manuscript does not discuss in detail the effects of discretisation effects on the ghost-gluon vertex and on the propagators. In particular, the propagators are not shown at all and they should be reported. This is of at most importance as it is well known [O. Oliveira, P. J. Silva, Phys. Rev. D86 (2012) 114513] that for the propagators the lattice spacing and the lattice volume should be properly chosen. A possible explanation of the observed differences could be due, at least partially, for the choice of lattice spacings and volumes where the simulations are performed
(iii) The finite volume effects, being due to the lattice spacing and to the lattice volume, are not discussed properly. This is also important as the number of lattice spacings and volumes reported on the manuscript varies significantly. For example, looking at the 3D simulations with lattice sizes of ~2 fm or ~ 3.9 fm, or 4D simulations with lattice sizes ~4.9 fm or ~9.8 fm, one can see clear differences between the various data sets for the various kinematical configurations. The grouping together of all the simulations data on Figs. 5 and 6 only makes their reading quite difficult. My suggestion goes to add the results for the same volumes separately. This can be done either as an inset on the figs. or by adding extra plots.
(iv) The section that worries me most being the Summary. I completely disagree with the authors summary. First, given the finite volume effects I hardly agree with what is written there. At most, would say that this study suggests that the comparison should be done with care and further studies are need before doing any conclusion. I cannot agree, in any way, with the second paragraph of the Summary. I recall the author that there are other interpretations [M. Tissier, Phys. Lett. B784 (2018) 146] and although the efforts associated with the scaling solution are an important work and contribution to the understanding of QCD, there is no evidence of these type of solution coming from lattice [probably the closest being A. Sternbeck, M. Mueller-Preuskker, Phys. Lett. B 726 (2013) 396].
The author should include all the above mentioned references in the revision.
In summary, I do think that the manuscript contains new and important contributions that can help in the understanding of QCD. It certainly, deserves to be published but I cannot agree with the present form of the manuscript and ask the author to review it.
See the report.