Probing Dark Sectors with Neutron Stars

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This review paper is devoted to probing dark sectors  with neutron stars. The paper  is carefully written,  is well structured, covers all aspects of the topic it develops and contains a large numbers of relevant references. I consider that this review will be very useful to the relevant scientific community. I highly recommend publication in the special issue

Author Response

We appreciate the referee’s careful consideration of our paper, and we note that the referee has no corrections for us to address.

Reviewer 2 Report

Comments and Suggestions for Authors

At present there appears huge amount of works about dark matter.  Many of them are not scientifically sound. Separation of  the Wheat from the Chaff  is important task whereas  simple listing of a  part of these works, as it is done in the given ms,  without their analysis seems me rather senseless  (about half of references, 86,  are cited already on  first 4 pages).

 In my opinion the review suffers from a lack of specificity.  I found only not motivated speculations that  something unknown can affect some observables. No specific constraints on observables are presented. So unfortunately,  for me at least, the review looks not informative. This year the authors have written two review papers [36], 81 pages, and [37], 84 pages, devoted to the same subject. The given review, 30 pages, largely repeats this material,  with a loss of informativity. Even many notations are not introduced. Although the ms. Is devoted to “Probing Dark Sectors with Neutron Stars”,  from the reference list containing 191 item I found only of order of two dozen  references  devoted to  description of neutron star interiors (see 168-170, 173-187 and several others). Review contains only 15  formulae. I should add that expressions (5)-(9) are not representative expressions which may help to understand essence of RMF models and why the latter  are used in application to neutron stars.  Why the authors focused attention namely on these expressions is unclear.

Concluding, I do not recommend publication.

Author Response

1 Response to Reviewer 2: universe-2759743
We have submitted this review article for publication within a special issue in Universe devoted to the neutron lifetime, which is of interest now because of the neutron lifetime anomaly and the possibility that processes involving new, weakly coupled particles, not present in the Standard Model of particle interactions, could explain it. This new focus emerged after different, simple new-physics models for explaining the anomaly were introduced by Fornal and Grinstein in 2018.
It was quickly noted, however, that these models could be severely constrained by the observed existence of neutron stars with mass in excess of about 0.7 solar mass. Thus our review explores the neutron star connection in depth and considers how both static and dynamical observations of neutron stars can constrain these models in different ways. We are not sure that the reviewer is aware of this background and context, so that it seemed to us that we should explain it.
We now address the reviewer’s remarks point by point. We present them in italics, followed by our response in plain text.
At present there appears huge amount of works about dark matter. Many of them are not scientifically sound. Separation of the Wheat from the Chaff is important task whereas simple listing of a part of these works, as it is done in the given ms, without their analysis seems me rather senseless (about half of references, 86, are cited already on first 4 pages). In my opinion the review suffers from a lack of specificity. I found only not motivated speculations that something unknown
can affect some observables. No specific constraints on observables are presented. So unfortunately, for me at least, the review looks not informative.
We do not see the value of discussing scientifically unsound papers. Rather, we discuss papers that are sound and are pertinent to the topic at hand. The referee is correct, though, in noting that we cite about half of our references in the first four pages of our article. There is an important reason for that. We believe the referee has happened upon it in saying “I found only not motivated speculations that something unknown can affect some observables.” We declare, rather, that dark matter and dark energy are concrete, that they have been observed beyond doubt, and that the baryon asymmetry of the universe (BAU) must also stem from physics beyond the Standard Model.
The puzzles of their dynamical origin are problems of major scientific importance. In the opening pages of our article we document this, we explain how models of the neutron lifetime anomaly could link to their explanation, and we note how these models connect to neutron-star structure and dynamics. It is incorrect to say that “No specific constraints on observables are presented.” Please note the discussion of pulsar constraints in Sec. 4 and the manner in which they appear within Fig.7-11, along with other experimental constraints noted there and elsewhere.
This year the authors have written two review papers [36], 81 pages, and [37], 84 pages, devoted to the same subject. The given review, 30 pages, largely repeats this material, with a loss of informativity. Even many notations are not introduced.
Reference [36] also contains much new material, and Ref. [37] is a regular journal article that has been accepted for publication in Phys. Rev. D. We note that the current article is on the same topic, though it by no means repeats previously published material. Rather, it attempts to present our detailed work within a broader context, in order to show the broad sweep of dark matter models that connect to explanations of the neutron lifetime anomaly and to explain the dynamical issues that come to bear in the interplay of dark-sector particles with neutron star dynamics.
Herewith we note symbols that we had used and had not defined — we have now rectified that, and here are the details. We now define Vij and GF in the opening page, me and f in Equation (1), and “UCN” and “PDG” in Figure 1. We also define “QCD” and “FLAG” later in that section. We have also added clarifying statements after Eqs. (10) and (13).
Although the ms. Is devoted to “Probing Dark Sectors with Neutron Stars”, from the reference list containing 191 item I found only of order of two dozen references devoted to description of neutron star interiors (see 168-170, 173-187 and several others).
We do not think that this is a fault. This is reflective of the field. We have found some additional references to include, and we believe we have included all the most pertinent references on the topic of our paper. We emphasize that the focus of our work extends beyond just the detailed description of neutron star interiors. It encompasses the effects of dark sector physics on neutron stars, which requires a foundational understanding of various related domains, including particle physics, astrophysics, and theoretical models beyond the Standard Model. In this regard, our reference list is curated to provide a holistic view, enabling readers to appreciate the multifaceted nature of the subject. The inclusion of references beyond the direct description of neutron star interiors is essential to offer a complete picture of the current understanding and theoretical exploration in
this area.
Review contains only 15 formulae. I should add that expressions (5)-(9) are not representative expressions which may help to understand essence of RMF models and why the latter are used in application to neutron stars. Why the authors focused attention namely on these expressions is unclear.
The critique concerning the number of formulas used in our manuscript suggests an emphasis on quantity over the relevance or significance of the expressions included. We believe that the essence of a scientific review lies not in the sheer number of formulas presented but in their pertinence to the topic and the clarity with which they convey the underlying principles. In this regard, our selection of formulas, particularly expressions (5)–(9), was deliberate and serves a critical purpose in our discussion.
As highlighted in our manuscript, the consideration of dense-matter phenomena is pivotal for understanding baryon interactions in neutron stars. In these environments, gravitational forces compress baryonic matter to extreme densities, pushing the system into the strongly repulsive domain of nuclear interactions. The elevation of ground state energies of baryons under such conditions is crucial for our discussion. It allows for decay processes that are kinematically forbidden in more standard settings, making neutron stars unique astrophysical laboratories for observing dark baryon decays.
Expressions (5)–(9) in our paper are specifically included to derive the energy spectrum of baryons in relativistic mean field (RMF) models. This is not just an incidental detail but one of the most important results discussed in our review. It directly relates to the high-density reach within neutron stars, which is essential for understanding the potential for new decay processes in these environments. We utilized these equations to plot the energy spectrum in Figures 7 and
8, highlighting how the center-of-mass (CM) energy in high-density regions exceeds the baryons’vacuum rest mass. This insight is pivotal for our argument, as it suggests the possibility of decay into states that are kinematically forbidden in vacuum.
Thus, our focus on these specific expressions is driven by their direct relevance to the core theme of our review. These equations set the stage for understanding how each neutron star, with its unique density profile, represents a distinct astrophysical laboratory.
Concluding, I do not recommend publication.
We hope we have persuaded the referee of the merits of our paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I have some technical comments/suggestions and hope that the authors take them into account or provide detailed answers.

1.       P. 1 “astrometric observations”. It is incorrect to call all the sets of the mentioned measurements “astrometric”. Better write “astronomical”.

2.       P.1 and the detections of neutrinos from extraterrestrial sources reveal nonzero neutrino masses

Here it is necessary to mention atmospheric neutrino measurements and quote corresponding papers (in the first place, the papers by Kajita et al.).

3.       The authors use notations that are not introduced. Even if a notation is standard in some fields of research, it is absolutely necessary to describe clearly EVERY variable (or term, or abbreviation) used in the text. E.g., “BNV” is introduced in P.11, but used already in PP. 9-10.

4.       P. 8 “ markedly below the mass of the most massive observed neutron stars, which exceed”.
References are necessary for the mass measurements.

5.       P. 9 “In the preceding section”
Unclear. Is it about Sec. 2.2, or Sec. 2.2.2, or what?
2.2 is a subsection. 2.2.2. is a subsubsection.

Please, check signs in eq. (9).

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English can be improved as the authors make lots of small mistakes like this one: “This is perspective differs”. Punctuation is also not appropriate (e.g., too many commas where they are not necessary).

Author Response

Response to Reviewer 3: universe-2759743

In what follows we reproduce the report verbatim in italics and note our response to its points in plain text.

Technical Comments and Suggestions

I have some technical comments/suggestions and hope that the authors take them into account or provide detailed answers.

1. P. 1 “astrometric observations”. It is incorrect to call all the sets of the mentioned measurements “astrometric”. Better write “astronomical”.

We have revised our manuscript and replaced the two instances of "astrometric" with "astronomical."

2. P.1 and the detections of neutrinos from extraterrestrial sources reveal nonzero neutrino masses

Here it is necessary to mention atmospheric neutrino measurements and quote corresponding papers (in the first place, the papers by Kajita et al.).

We respectfully point out that we have done this in citing Ref.~[18]. Although T.~Kajita was spokesperson of that experiment, Fukuda was first author of the pertinent paper. Please note \url{https://physics.aps.org/articles/v8/97} for further discussion of this point.

3. The authors use notations that are not introduced. Even if a notation is standard in some fields of research, it is absolutely necessary to describe clearly EVERY variable (or term, or abbreviation) used in the text. E.g., “BNV” is introduced in P.11, but used already in PP. 9-10.

We have reviewed the updated manuscript to ensure that all notations, including terms and abbreviations, are introduced and clearly defined at their first point of use.

4. P. 8 “ markedly below the mass of the most massive observed neutron stars, which exceed”.
References are necessary for the mass measurements.

We added the references for the three most massive neutron stars with masses above 2 M⊙ in our updated manuscript.

5. P. 9 “In the preceding section” Unclear. Is it about Sec. 2.2, or Sec. 2.2.2, or what? 2.2 is a subsection. 2.2.2. is a subsubsection.

We replaced “In the preceding section” with “In section 2.2,. . . .”

Please, check signs in eq. (9).

We have checked the signs in Eq. (9) to confirm their accuracy. The first equality is the length of the momentum four-vector, a Lorentz invariant quantity, signifying it remains consistent with the rest mass of baryons in vacuum. The second portion of Eq. (9) emerges directly from substituting
Eq. (8) into its first part.

Comments on the Quality of English Language
English can be improved as the authors make lots of small mistakes like this one: “This is perspective differs”. Punctuation is also not appropriate (e.g., too many commas where they are not necessary).

We have revised our manuscript by correcting minor errors.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

 As I see the authors  did not answered my critics. I think in my previous referee report I clearly explained my points.  I see that in new version authors just formally enlarged reference list.  So, I remained with opinion explained in my previous referee report.