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Speed of sound in dense strong-interaction matter
by Jens Braun, Andreas Geißel, Benedikt Schallmo
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Submission summary
| Authors (as registered SciPost users): | Jens Braun · Andreas Geißel |
| Submission information | |
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| Preprint Link: | scipost_202211_00010v1 (pdf) |
| Date submitted: | 2022-11-04 13:46 |
| Submitted by: | Braun, Jens |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the speed of sound in strong-interaction matter in density regimes which are expected to be governed by the presence of a color-superconducting gap. At (very) high densities, our analysis indicates that the speed of sound approaches its asymptotic value associated with the non-interacting quark gas from below, in agreement with first-principles studies which do not take the presence of a color-superconducting gap into account. Towards lower densities, however, the presence of a gap induces an increase of the speed of sound above its asymptotic value. Importantly, even if gap-induced corrections to the pressure may appear small, we find that derivatives of the gap with respect to the chemical potential can still be sizeable and lead to a qualitative change of the density dependence of the speed of sound. Taking into account constraints on the density dependence of the speed of sound at low densities, our general considerations suggest the existence of a maximum in the speed of sound. Interestingly, we also observe that specific properties of the gap can be related to characteristic properties of the speed of sound which are indirectly constrained by observations.
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Reports on this Submission
Anonymous Report 1 on 2023-12-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00010v1, delivered 2023-12-05, doi: 10.21468/SciPost.Report.8225
Report
The authors discuss the speed of sound at zero temperature in ultra-dense matter, in particular the effect of a color-superconducting gap. The full behavior of the speed of sound at nonzero chemical potential is unknown and has been discussed from various different angles in recent years. In particular, it is of relevance for the understanding of matter inside neutron stars. The manuscript adds an interesting and carefully discussed aspect to this area of research. The authors put together results from previous work in an original way and obtain interesting and novel results. The manuscript is mostly written in a clear and understandable way. I do have a few questions that I think the authors should address before publication:
(1) The authors neglect quark masses without really commenting on this approximation. Of course, the quark masses become negligibly small at high densities, but so does the color-superconducting gap. So is it clear that they would not change any of the conclusions? Since they will effectively be functions of the chemical potential it seems to me they could in principle have an effect on the speed of sound.
(2) I have a few questions about Fig 1: As mentioned in the text, the pQCD gap increases with mu (below Eq (13)); why is this not reflected in the weak-coupling curve in the upper panel? Also, from looking at the different scales for the 2 curves, it seems the fRG result does not approach the weak-coupling result at high densities. Is that correct? Maybe a comment and explanation would be helpful.
(3) I think it might be useful to mention that all results only hold for zero temperature already before the first paragraph of sec II. T=0 is already needed for Eq (1) and possibly it would even be useful for the reader to mention T=0 in the abstract.
(4) The authors argue that gap effects for n>n_min are negligible while they are important for n<n_min (page 6 and conclusions). This statement seems a bit imprecise to me since it is not based on any power counting, or is it? Looking at, say, the purple curve in the left panel of Fig 2, the deviation from the Delta=0 curve at n_min is already as large as the added deviation below n_min at the end of the scale. So I am not sure why n_min would play any role as a threshold for the power counting. Perhaps this statement can be made more precise.
(5) The authors rightly emphasize that the gap gives rise to a speed of sound larger than the asymptotic value and thus supports the expectation of a maximum in the speed of sound predicted on phenomenological grounds. Is the gap the only known physical effect that can yield this behavior in the high-density regime? For instance, if the quoted fRG study is repeated without the gap, would some pure interaction effects be able to produce a similar increase in the speed of sound? The result of the paper could be made even stronger if a short discussion would be added.
(6) In the conclusions, the authors mention that strange quarks are relevant for astrophysical applications. But even from a purely theoretical point of view, strange quarks (and all heavier flavours in principle) should appear at the densities considered here. The authors do mention earlier that 2+1 flavours are the "most relevant" case, but I would think a few more comments would be helpful here. For instance, at asymptotic densities we expect CFL rather than 2SC that is considered here. Would we expect any of the results to change qualitatively in that case?