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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:  https://arxiv.org/abs/2210.07597v1 (pdf) 
Date submitted:  20221020 12:53 
Submitted by:  Horak, Jan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational, Phenomenological 
Abstract
We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospinsymmetric approximation. We employ spectral DysonSchwinger equations and compute the nonperturbative quark propagator directly in realtime, 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 timelike 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 quarkgluon 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 abinitio calculation of transport as well as resonance properties in QCD.
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Reports on this Submission
Anonymous Report 1 on 2023424 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2210.07597v1, delivered 20230424, doi: 10.21468/SciPost.Report.7099
Report
1) Condition (9) needs further clarification and support by explicit examples. I strongly recommend adding a figure to demonstrate (9) for one or two example cases. In particular, it would be interesting to use a quark propagator with an analytic structure as shown in Fig. 3.9 (right) of https://arxiv.org/abs/1606.09602 or as discussed in https://arxiv.org/abs/1612.06002 or https://arxiv.org/abs/1312.2721.
2) Again concerning (9), please clarify how \omega_0 is computed and whether the actual pole position needs to be known for this extraction. Maybe an example would be useful here too.
3) Concerning Fig. 1 and 2: Please use the standard representation of DSEs as widely used in the literature. In particular, use "1" for bare and dressed propagators and use full propagator symbols and vertices for the last diagram on the righthand side.
4) Assumption (10) is central and needs to be mentioned in the abstract as well as in the introduction.
5) Before (21), please cite an appropriate source for the "mild momentum dependence" of scattering kernels, possibly https://arxiv.org/abs/1610.06158.
6) A long discussion precedes the simple choice made in (22). This, again, is a central assumption and needs to be mentioned more prominently, such as in the abstract and the introduction, or at least in the beginning of the section.
7) The last sentence in the caption of Fig. 4 ("attributed to the use of a classical quarkgluon vertex...") is misleading. Why should this be expected? Please clarify this statement and add appropriate references to support it.
8) In section V, it is written that the "investigation represents a ... major step...". It would be more appropriate to say that the "investigation represents a ... major technical step..." as the employed model is yet too simple to have any farreaching physical consequences.
9) Similarly, it is written that the "results have a wide range of ... applications". It would be more appropriate to say that the "technique developed here has the potential of allowing for a wide range of ... applications in the future", or similar. The results presented here are still based on a rather simple model and certainly should not be used for any realistic computations.
Author: Jan Horak on 20230712 [id 3803]
(in reply to Report 1 on 20230424)Reply referee report
We thank the reviewer for the suggestions and believe that they have substantially improved the paper. Below, we reply to their comments as numbered in the report.
1) Eq. (9) represents an empirical finding, as explicitly stated below the equation. We present a simple analytic example, fulfilling (9), in Appendix A, as stated in the paragraph above. The mentioned reference (1612.06002) is already cited in the manuscript, see [58] in the previous version.
2) \omega_0 is implicitly defined by (9) through the second part of the equation. To make this more explicit, we state this just below the equation in the resubmission.
3) The notation used in Fig. 1 is defined in Fig. 1, and has been used before in a series of publications (https://arxiv.org/abs/2006.09778, https://arxiv.org/abs/2103.16175, https://arxiv.org/abs/2202.09333). It allows for consistency with notation in other functional approaches, such as the functional renormalization group. There full propagators are not marked by blobs, and inverse full propagators, being full twopoint functions, as colored blob with two legs. Both functional frameworks are used in our group, and we wish to employ a unique, consistent diagrammatic notation.
4) We added a sentence in the introduction, mentioning the analytic poletail split. Since we consider this to be a calculational, technical detail, we decided against mentioning this in the abstract.
5) We added the mentioned and two further references.
6) We added a comment mentioning the approximation (22) in the introduction in the resubmission.
7) The statement is discussed in the mentioned Appendix C, where also references are provided.
8) & 9) We made minor modifications to the formulations as suggested by the referee(s).
However, we are surprised by the assessment that our work only constitutes a technical development and the approach is not ready for applications.
In our opinion, the technical development has been done in https://arxiv.org/abs/2006.09778, and underlies our present computation. Furthermore, we believe that our work does allow directly for applications such as the computation of observables. In fact, we are currently working on some.
One is possibly inclined to compare our truncation with those used in Euclidean computation. In our opinion this is not a very meaningful comparison since our work focusses on the real frequency axis. It is wellknown from, e.g., bound state studies that DSEs typically have to be solved within less advanced approximations due to the increased difficulties for realtime or timelike computations. For example, commonly used vertex models in Euclidean computations such as the MarisTandy model are not applicable due to their unphysical complex singularities.
We have demonstrated in a recent work (https://arxiv.org/abs/2301.07785) how spectral functions for vertices can be obtained from lattice data, which allows the incorporation of full vertices in our spectral DSE setup and in consequence a systematic improvement of our truncation.
On top of that, we ask the referee to bear in mind that our truncation includes a full 2+1 flavor QCD gluon propagator, which supersedes the common choices for the gluon propagator, e.g., in the MarisTandy model.