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On the quark spectral function in QCD
by Jan Horak, Jan M. Pawlowski, Nicolas Wink
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Submission summary
| Authors (as registered SciPost users): | Jan Horak · Jan M. Pawlowski · Nicolas Wink |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202307_00019v1 (pdf) |
| Date submitted: | 2023-07-12 14:20 |
| Submitted by: | Horak, Jan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational, Phenomenological |
Abstract
We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole structure at time-like momenta larger than the propagator's gapping scale as well as a negative scattering continuum. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.
List of changes
- added an explanation of \omega_0 below eq. (9)
- we added a comment mentioning the approximation (22) in the introduction
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2023-7-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202307_00019v1, delivered 2023-07-27, doi: 10.21468/SciPost.Report.7569
Report
I thank the authors for their response and for taking some of my suggestions into account. However, the following points still need to be addressed before I can recommend publication.
1) I still believe that the quality of the paper would strongly benefit from adding an explicit (analytic and numerical) example to illustrate condition (9) based on one of the standard propagators from the literature which has a well-known analytic structure, for example as shown in Fig. 3.9 (right) of https://arxiv.org/abs/1606.09602 or discussed by Alkofer-Watson-Weigel (Phys. Rev. D 65, 094026). If the discussion in Appendix A covers such a case, this should be mentioned and substantiated by explicitly using the corresponding numerical parameters.
3) If the authors insist on using this graphical notation, it should at least be justified in the paper and clearly mentioned that this deviates from the wide-spread convention in the literature, in order to avoid confusion of the reader.
4) Concerning my request to mention (10) already in the abstract, the authors respond that "Since we consider this to be a calculational, technical detail, we decided against mentioning this in the abstract."
However, in the manuscript, below Eq. (10), it is written that "Equation (10) represents a central approximation of this work."
If it is so central, it must be mentioned in the abstract.
Author: Jan Horak on 2023-07-31 [id 3853]
(in reply to Report 1 on 2023-07-27)We thank the reviewer for the additional suggestions. Below, we reply to their comments as numbered in the report.
1) To accommodate the referee’s request for an explicit example of the condition (9), below (9), we added a summary of the discussion of Appendix A.
We hope that the readers will be able to convince themselves that the roots of
lie on the first/second Riemann sheet for the +/- case, and that this example does not require visualisation.
2 ) To avoid confusion, we added a comment that in contrast to other diagrammatic notations, in our notation full propagators do not carry blobs and the inverse bare propagator is simply given by a dot with two legs.
In our opinion, the only requirements for notation are clarity and consistency–both of which are fulfilled in our case. Beyond that, notation should be completely up to the authors.
3) We added a subsentence mentioning the approximation (10) in the abstract.