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Dark matter from the centre of SU (N )
by Michele Frigerio, Nicolas GrimbaumYamamoto, Thomas Hambye
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Submission summary
Authors (as registered SciPost users):  Michele Frigerio · Nicolas GrimbaumYamamoto 
Submission information  

Preprint Link:  scipost_202302_00014v1 (pdf) 
Date submitted:  20230207 21:30 
Submitted by:  Frigerio, Michele 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Phenomenological 
Abstract
A dark sector with nonabelian gauge symmetry provides a sound framework to justify stable dark matter (DM) candidates. We consider scalar fields charged under a $SU(N)$ gauge group, and show that the centre of $SU(N)$, the discrete subgroup $Z_N$ also known as $N$ality, can ensure the stability of scalar DM particles. We analyse in some details two minimal DM models of this class, based on $SU(2)$ and $SU(3)$, respectively. These models have nontrivial patterns of spontaneous symmetry breaking, leading to distinctive phenomenological implications. For the $SU(2)$ model these include a specific interplay of two DM states, with the same interactions but different masses, and several complementary DM annihilation regimes, either within the dark sector or through the Higgs portal. The $SU(3)$ model predicts dark radiation made of a pair of dark photons with a unique gauge coupling, as well as regimes where DM semiannihilations become dominant and testable.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023320 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202302_00014v1, delivered 20230320, doi: 10.21468/SciPost.Report.6931
Report
The origin of DM stability is a key issue in DM model buildings and phenomenology. This manuscript addresses this issue, assuming that DM is stable due to Nality of nonAbelian dark SU(N) gauge symmetry. This is a generalization of KraussWilczek mechanism of $U(1)$ gauge symmetry to the nonAbelian cases and makes an interesting possibility for DM stability. The materials in the manuscript are original, useful and interesting enough. The manuscript is well organized with no grammatical problem. Most parts of the manuscript are clearly written. The manuscript is worth to be considered for publication in SciPost. Before I recommend the acceptance of this paper, I would suggest the authors address some minor issues that are described below.
1. In the overview of the earlier works in the Introduction, the authors review earlier literature on the DM stability in terms of gauge symmetry. However, there is no clear distinction whether DM is stabilized by global or gauge symmetry (I guess they meant local gauge symmetry). I would suggest that the authors make two categories of DM models more clearly, where DM is stable (or long lived) because of global or local dark gauge symmetry and add relevant references according to these two categories. For example, Ref. [9] is about scalar DM models, based on global $Z_2$ and $Z_3$ symmetries. Local symmetry versions of $Z_2$ and $Z_3$ (both model construction and detailed phenomenology) were presented in detail, for example, in https://arxiv.org/abs/1407.6588 and https://arxiv.org/abs/1402.6449, respectively. Underlying philosophy and DM phenomenology in DM models with global and local dark gauge symmetries are vastly different in terms of particle contents: dark Higgs boson and dark photon. And these two categories of global vs. local dark gauge symmetries are better to be clearly distinguished. There could be similar cases in Introduction and other sections, and appropriate changed are recommended.
2. The main motivation for this manuscript is the origin of DM stability. But DM decays from dim5 and dim6 operators induced by gravity are not addressed clearly in case of dark symmetry is global. For example, in https://arxiv.org/abs/1303.4280, it was noted that global symmetry would be generically violated in the presence of gravity, and electroweak mass scale DM would decay too fast through gravityinduced dim5 operators, and cannot make a good DM of the Universe. This problem could be evaded if one considers local dark gauge symmetry, instead of global dark symmetry. It would be nice to include this discussion in Introduction, since it will strengthen the importance of the proposal made in this manuscript.
3. In Sec. 3.1, the authors discuss in brief monopole DM, summarizing the work by Murayama and Shu, who discussed topological monopole DM without explicit construction of the model. The explicit model was constructed in Ref. [19] ( https://arxiv.org/abs/1311.1035 ), and it was shown that multicomponent dark sector with massive vector DM, monopole DM and massless DR arises from spontaneous dark gauge symmetry breaking, $SO(3)_D \rightarrow U(1)_D$. In the manuscript, Ref.[19] is cited only in the context of massive vector DM. It would be nice to mention [19] in the paragraph on monopole DM in the earlier part of Sec. 3.1.
4. Sec. 4.2 and Sec. 5.3 discuss the case $SU(3)_D$ broken to $U(1)_3 \times U(1)_8$. In this case, there is no selfinteraction among the DR, and no constraints from large scale structure (see, for example, [1609.02307] Residual NonAbelian Dark Matter and Dark Radiation (arxiv.org) , which could be cited along with Refs. [18,19,20,21] since the model there is qualitatively different from Refs.[1821]). If the unbroken gauge group is nonAbelian as described in the above reference, the gauge coupling should be very tiny and thermal WIMP scenario or SIDM cannot be realized. Otherwise, there would be too much suppression of the matter power spectrum in small scales (large $k$ region), in disagreement with the observation. It would be important and interesting to know if the symmetry breaking patterns for $SU(N>3)$ can be nonAbelian or simply products of U(1)’s. If the latter is the case, the proposal in this manuscript would get another strong point, since one can avoid stringent constraints from cosmology on matter power spectrum.
Report #1 by Anonymous (Referee 1) on 2023313 (Contributed Report)
 Cite as: Anonymous, Report on arXiv:scipost_202302_00014v1, delivered 20230313, doi: 10.21468/SciPost.Report.6891
Strengths
1. The paper focuses on the important question of stability of DM.
2. The analysis is detailed and systematic.
3. The paper is clearly written.
Report
The stability of DM is an important question that the paper focuses on. It builds a new class of models based on $SU(N)_D$ gauge groups. After symmetry breaking, a residual $Z_N$ symmetry stabilizes the DM particles. The paper is worthy of publication. However, there are a few places where the discussion could be improved.
Requested changes
1. In sec 5.1 it would be useful to clarify that the dark sector and the SM are assumed to be in thermal equilibrium at very early times, if that is the assumption the authors are making to compute $\Delta N_{\rm eff}$.
2. On page 17, just above sec 5.2.2., it would be useful if the authors expand on the `ellipticity constraint' for the discussion to be self contained.
3. In sec 5.3.2, the authors describe various signatures from semiannihilations. It would be useful to know whether some of those constraints actually constrain the parameter space in Fig. 6 where only overclosure and unitarity bounds are shown.
4. In Fig. 5 top panel, there is a region of parameter space where relic density can be successfully explained without running into other constraints. I am wondering whether the authors could briefly comment on whether and to what extent future direct detection experiments can be sensitive to the remaining parameter space on the orange line.