AMS-02 antiprotons and dark matter: Trimmed hints and robust bounds

1- Detailed discussion of analysis strategy and clear presentation of results
2- Careful treatment of experimental and theoretical uncertainties
3- Methodology sets the standard for any future analysis of AMS-02 anti-proton data

1- Discussion of results from the literature could be more pedagogical
2- Not all approximations are sufficiently justified, analysis might be overly conservative
3- Most results not new, considered data set somewhat outdated

In the manuscript "AMS-02 \bar{p}’s and dark matter: Trimmed hints and robust bounds" the authors weigh in on the important discussion about the interpretation of the AMS-02 anti-proton data in the context of dark matter annihilation. Over the past years, there have been various claims regarding the evidence of a dark matter signal in this data set (and its significance) and how the data can be used to constrain dark matter models.
In this context, the present work emphasizes the need of an accurate treatment of experimental and theoretical uncertainties, which substantially reduce the significance of the dark matter excess and allow robust bounds to be obtained (there’s the respect!). At the same time, the authors emphasize the need for efficient analysis strategies that do not waste time and resources (although it does not always become clear how much more computationally expensive a more detailed analysis would be, see also below).
I find the paper extremely well written and very enjoyable to read. The authors are clearly world-leading experts on the topic, and their experience and authority is highly welcome. I very strongly agree with the central point of this paper, which is that an accurate treatment of uncertainties (and their correlations) is essential. Although no substantial new results are presented and the data set under consideration is already outdated, it is very important for the community to have such a careful and detailed analysis. I expect the paper to be suitable for publication in SciPost once the authors have clarified whether their treatment of uncertainties is indeed accurate rather than conservative. Specifically, I would ask them to address the following comments.

Major comments:
1- The authors have written many previous publications on related topics and sometimes seem to assume that the reader is familiar with most of them. I find this most striking in the context of the covariance matrix for theoretical uncertainties, for which no details are provided and the reader is simply referred to ref. [36]. I think it would be important to briefly review the key elements of this approach and its justification (and make an effort to reduce the overall number of places where the reader is forced to consult another paper to understand the analysis).
2- The authors take a significant shortcut in their analysis by assuming that theoretical uncertainties can be represented by a covariance matrix that can be added to the one describing correlations in experimental data. Doing so is clearly conservative, in the sense that error bars increase and hence the preference for (or evidence against) any signal hypothesis is reduced. A more realistic treatment should instead associate the theoretical uncertainties with the signal prediction, for example by introducing nuisance parameters that are profiled out at each step. I don't think such an approach needs to be computationally very expensive (see e.g. https://cds.cern.ch/record/2242860). Crucially, using nuisance parameters to encode systematic uncertainties may increase rather than decrease the significance of a local excess, if the nuisance parameters can be adjusted in such a way that they improve the fit of the excess.
3- An important aspect of the present work is that it no longer uses the MIN-MED-MAX scheme advertised by some of the authors in previous studies (see e.g. arXiv:2103.04108). It would be good to clarify whether the authors now consider this scheme inappropriate for scrutinising the AMS-02 anti-proton data and would discourage its use, or whether they expect that it would lead to largely similar results. Along similar lines, the appendix of arXiv:2103.04108 advertises the use of a covariance matrix to capture the effect of uncertainties in propagation parameters. Would it not be possible to use this approach in the present work?
4- It remains unclear why the QUAINT propagation scheme leads to weaker constraints than the BIG propagation scheme, even though the latter has more free parameters and should therefore in principle give less tight bounds. A short discussion of this should be added.

Minor comments:
1- Since the authors have chosen to use fairly mathematical language to describe their statistical approach, I would like to add that Wilks theorem does not apply if the null hypothesis lies at the boundary of the parameter space and one needs to use Chernoff's theorem instead (see https://arxiv.org/pdf/1407.6617.pdf). As a result, the critical value of Delta chi^2 corresponding to a 95% confidence level exclusion is reduced from 3.84 to 2.71.
2- The plots comparing the present work to previous studies are very important, but quite inconvenient for the reader, as the text never connects the author names (used in the plot legend) to the bibliography entry. I would suggest making this connection explicitly in the figure caption or in the main text.
3- In order to enable a better comparison with the literature in figure 6 it would be more appropriate to use the QUAINT rather than the BIG setup.
4- It is not clear why the bound for the WW final state stops at m_chi = m_W, given that annihilation can also proceed through an off-shell W boson. This bound should be extended if possible.

1. Excellent evaluation of the way the treatment of errors impacts the significance of a dark matter signal.
2. Sensible discussion of robust procedures for assessing local significance, with cautionary words about simplistic error analyses.
3. Up-to-date cosmic ray propagation models used.
4. Useful and reliable indirect detection limits on the dark matter annihilation cross section are calculated and presented in the plots.

This manuscript makes a very useful addition to the literature on dark matter indirect detection signals. The analysis is robust. The results are interesting and relevant. I have no hesitation in recommending publication.