Dark Matter in Anomaly-Free Gauge Extensions

We thank the referees and the editor for the useful and constructive remarks and criticism on our paper. Together with this report, we submit a revised version of our manuscript taking into account the points raised by all referees. We address them in order. In doing so, we summarize comments on the same subject from the editor and both referees. (Referee/Editor suggestions are in double quotes).

"Please tighten up the presentation of model in Secs 2 and 3, in particular shorten considerably the discussion of the U(1)_{B-L} model and only refer to it. You may want to shift some of the derivations verbatim to appendices, as one of the referees suggested. "

We considerably shortened the discussion in Section 2 and further follow the recommendation of referee 2

"1- Streamline Introduction

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."

and streamline the introduction, move all non-essential steps in the new Appendix A and merge Sections 2&3.

We consider the discussion of the U(1)B-L model in the new Section 2 as essential to explain the motivation for discarding this model later. We understand the criticism that this might suggest an equal treatment of the three models during the rest of the paper and we therefore put a clarifying statement already in the introduction:

'We argue that searches for missing energy signals at the LHC are particularly powerful for two of these models, namely the $U(1)_X$ and the $U(1){L\mu-L_\tau}$ gauge groups. After deriving the properties of the mediators for the three classes of models defined above, we focus our analysis on these two models. '

"2 Also shorten the discussion of bounds in Secs. 4,5 by summarizing the findings of the previous studies quoted there. Please take into account the comment of one of the two referees ("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→4μ search can be more powerful than the trident bound in certain regions of parameter space."). "

Even though many of the constraints discussed in Section 4 and 5 are not new, we consider it important to explicitly state what constraints we include in our analysis (and in the plots). To the best of our knowledge a comparative study of all the different models discussed in this section has not been presented elsewhere. We therefore only streamline these sections in a minor way in the revised submission.

Referee I is right in pointing out that the Z -> 4mu search at CMS provides stronger constraints for the L_mu-L_tau gauge boson for masses m_Z’ < 60 GeV. This is outside the interesting parameter space for our analysis and the region shown in Fig.5 and we state so explicitly in the revised version.

"3. Please respond to the referee comment concerning the number of signatures for the Z' as DM mediator."

The Referee is right that this sentence in the introduction of Section 5 omitted the last subsection of this part of the paper. In the revised version we explicitly refer to the third part of this section:

'In the case of very small mixing angles the production cross section of the $Z'$ can become smaller than the production cross section of the scalar $S$, whose decays are dominated by the $S\to Z'Z'$ decay rate. We present a third discovery strategy based on the process $S\to Z'Z'\to \mu^+\mu^- \met$.'

"4. Please detail how you modified the matrix code."

'The matrix code is used to derive the NNLO production cross section for the Z boson at the LHC and we use the corresponding K factor to account for corrections to the Z’ production cross section. Since the production cross section for the U(1)X and the U(1) gauge boson are only produced through kinetic mixing with the Z at the LHC, this estimate should be good. We added an explanatory sentence in the revised version.'

"5. Please make statements concerning uncertainty estimates more explicit, as one of the referees suggested.

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."

In the appendix discussing the details of the shape analysis, we explicitly state

'Clearly, the separation between the hypotheses and thus the final confidence level is extremely sensitive to the modeling of systematic uncertainties.'

"6. Please check, again, for typos."

We thank the referees for pointing out the typos, and hope we have eliminated all of them.

We hope that after addressing all points raised by the referees, our paper will be considered fit for publication by SciPost.

see comments.