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On the complex structure of Yang-Mills theory
by Jan Horak, Jan M. Pawlowski, Nicolas Wink
|Authors (as registered SciPost users):||Jan Horak · Jan M. Pawlowski · Nicolas Wink|
|Preprint Link:||scipost_202209_00032v3 (pdf)|
|Date submitted:||2023-09-21 16:12|
|Submitted by:||Horak, Jan|
|Submitted to:||SciPost Physics|
We consider the coupled set of spectral Dyson-Schwinger equations in Yang-Mills theory for ghost and gluon propagators. Within this set-up, we perform a systematic analytic evaluation of the constraints on generalised spectral representations in Yang-Mills theory that are most relevant for informed spectral reconstructions. Furthermore, we provide numerical results for the coupled set of ghost and gluon spectral functions for a range of potential mass gaps of the gluon, while allowing for small violations of the spectral representation. The analyses are accompanied by thorough discussion of the limitations and extensions of the present work.
Author comments upon resubmission
List of changes
- Further explanation to clarify distinction between the common loop expansion in the CF model and functional approaches to YM theory, including the interpretation of the gluon mass parameter and BRST invariance in section V, just above section V.A
Submission & Refereeing History
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Reports on this Submission
I plainly agree with the report of referee 1. I cannot recommend publication because the points adressed in the first two reports by both referees were not sufficiently adressed. There are valuable calculations in the article, but the authors fail to put them in the right context.
I agree entirely with the last report of the other referee (Report 2 on 2023-9-12), but I do not see any real improvement in the last version.
In my opinion, in the new (third) version, the authors did not manage to clarify point (1) of that report. That point was also one of my main criticisms and it was the minimal effort which was expected for publication. Thus, I cannot recommend publication in the present form.
Actually, the authors still refuse to answer a very simple question which was raised by both referees:
"if they would have started not from a YM model, but a CF model, would they have had a different outcome?"
I do not think so.
In the new comments, above Sec. V-A, the authors admit that the difference between CF and YM would be the "interpretation" of the mass parameter: the mass is a free parameter in CF, while it is tuned in YM by a procedure
which aims "at eliminating the introduced gluon mass parameter and restoring BRST invariance".
However, in the numerical calculations, the equations are solved "for a family of input gluon mass parameters". It does not seem that the mass is fixed by restoring BRST. Even in the figures, it seems that different values of the mass parameter are discussed, as a free parameter. Thus, according to that "interpretation" the model which is studied is CF.