Dark Matter in Anomaly-Free Gauge Extensions

1. The main topic of the paper (dark matter in gauge extended models) is interesting.

2. The discussion of the mono-jet shape analysis (and its comparison with the cut and count analysis) and of the possibility to establish the link between a $Z^\prime$ and dark matter (even in the presence of $Z^\prime$ decays to invisible neutrinos) is novel and interesting.

1. The discussion of the several bounds (Secs. 4, 5) is not particularly novel and it mainly summarizes many results already reported in the literature.

2. The presentation of the $U(1)_{B-L}$ model is rather misleading: the authors drop this model after an initial short discussion.

The paper discusses dark matter models based on new anomaly-free symmetries which include a fermionic dark matter, a new $U(1)$ gauge boson and a scalar giving mass to the corresponding $Z^\prime$. The authors analyze the several bounds coming from dark matter experiments, as well as colliders and low energy experiments. Furthermore, they compare LHC shape and cut and count analyses to probe the nature of the $Z^\prime$.

1. The presentation would improve if the authors shorten a bit the discussion of the models in Secs. 2,3 and of the bounds in Secs. 4,5 since these sections are not particularly novel.

2. At the end of Sec.4, the authors should change the discussion of the LHC $Z\to4\mu$ bound. As shown in their Ref. 34 (1406.2332) and Ref. 19 (1511.04107), as well as in the corresponding CMS analysis http://inspirehep.net/record/1676064/files/EXO-18-008-pas.pdf the $Z\to4\mu$ search can be more powerful than the trident bound in certain regions of parameter space.

Overall, the paper is very timely and of decent quality. Various formulae are explicitly derived and discussed. Also the level of the numerical studies performed is adequate. Thus in principle I support the publication in SciPost. As far as I can see the considered limits are indeed the relevant ones and the presentation of possible signatures is adequate. In particular the quantitative estimate obtained by a shape analysis instead of a cut-and-count analysis in the monojet phase-space is interesting.

There are a few minor weaknesses in the presentation of the results and I invite the authors to address these issues.

1-The information density of the paper at hand is quite high (which of course is not necessarily a weaknesses, see above), however the readability of the paper would strongly profit moving some of the detailed derivations to appendices. I invite the authors to implement such changes, as detailed below.

2- The Introduction is partly hard to comprehend. For example I do not understand the relevance of the abrupt sentence "Even if we model our dark matter candidate after the supersymmetric neutralino..."

3- The paper introduces three U(1) models, however very early on in the discussion of relevant limits, one of them turns out to be basically excluded (the B-L model) and the authors state: "This is why at this stage we will drop the U(1)B−L gauge group (and any other group with gauged electrons) from our analysis.". Still, later on again constraints for the B-L are discussed.

4- I do not understand how the program MATRIX is used in the analysis at hand. The authors state: "We compute the Z′ production cross section with MadGraph5 [43], accounting for higher order corrections using Matrix ". To the best of my knowledge the MATRIX Monte Carlo does not provide predictions in any Z' model.

5- There are several typos in the manuscript, starting from the very first sentence: "The nature of dark matter is one the great mysteries", amongst others also including "This setup is by trivially free of anomalies" on page 4 and "the the" on page 15, "gauge bosons the LHC production cross section" on page 17.

The paper introduces three models for particle dark matter based on a spin-1/2 dark matter candidate and a spin-1 mediator. The authors argue that such models should be anomaly free and should also introduce an additional scalar from gauge boson mass generation. In this war the authors suggest that several simplified models used as benchmarks for ongoing Dark Matter searches are inconsistent and incomplete. The authors discuss various theoretical and experimental limits and show that large parts of the spin-1 parameter space is excluded once consistent models are introduced. In particular they consider three signatures that can arise at the LHC.

Following the listed weaknesses above I suggest to

1- Streamline Indoduction

2- Move detailed derivations to appendices, in particular from Section 2.

3- Sections 2 & 3 should be merged, they both discuss the phenomenology and motivation for the three models.

4- Already in this new Section 2 (see above) it should be mentioned that the B-L is basically excluded. In fact I don't necessarily see the point this model is discussed in great detail including several Figures.

5- The use of the code MATRIX should be clarified.

6- At the beginning of Section 6 the authors state: "We follow two strategies to establish the Z′ as a dark matter mediator: a profile analysis of the di-lepton mass peak [63] and a combination with the mono-jet signal." In fact there is a third signatures being discussed in Section 6.3.

7- The authors should state clearly that a realistic uncertainty estimate of the proposed shape analysis is highly non-trivially due to the nature how the monojet backgrounds are constrained.

8- Fix typos