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Review on Goldstone dark matter

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Abstract

We review the theory and phenomenology of models in which the dark matter is made of composite pseudo-Nambu Goldstone bosons. We focus predominantly on models in which the Higgs is also composite and dark matter is a singlet and heavier than the Standard Model fields. Then we discuss a variety of departures from this main setup, including: electroweak charged dark matter, lighter dark matter, issues related to quantum anomalies, ultraviolet completions or composite dark matter not related to the hierarchy problem.

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Notes

  1. As we have seen in previous sections, CHMs can shed light on the gauge hierarchy problem as well as on the flavour problem. We also highlight again in this section that they can be much more predictive than other models.

  2. The following toy example should illustrate this conflict. Consider the function \(f(x,y) = A (x-y)^2\). This function is trivially invariant under the shift \(x\rightarrow x+\alpha \), \(y\rightarrow y+\alpha \). However, this symmetry is broken if \(x\rightarrow -x\) is enforced, unless \(A=0\). A similar conflict in the composite DM model could require \(L_\sigma = 0\) and therefore no DM propagating field.

  3. While \(\mathrm{SO}(6)/\mathrm{SO}(5)\) fulfils this condition, \(\mathrm{SO}(5)\times U(1)/\mathrm{SO}(4)\) must be parametrised by two scales f and \(f_S\), unless \(f_S\gg f\) as we often assume for simplicity. Similar considerations apply to \(\mathrm{SO}(6)/\mathrm{SO}(4)\) and \(\mathrm{SO}(7)/\mathrm{SO}(5)\).

  4. Despite being presumably negligible for pNGBs, it is worth to mention that interpreting experimental data in the context of composite DM might be more subtle than in the elementary case for several reasons. The limits reported by experimental collaborations usually assume that the DM-nucleon cross section is independent of the recoil energy; i.e. it depends only on the nucleon form factor. This is however not true for composite DM [28, 29]. In turn, theoretical estimations of the DM form factors are challenging and rely typically on the lattice [30]. Likewise, the DM velocity distribution and profile in models of composite DM could be appreciably different from that assumed by the experimental collaborations [31].

  5. In Ref. [12] it was shown that the DM phenomenology of this model can be still captured by the parametrisation in Eq. (8) with \(a_1,a_2,a_3=31/(75\sqrt{2} )\sim 0.3\) and \(\gamma \) and \(\delta \) being, as usual, dependent on the fermionic couplings.

  6. In the simpler coset \([\mathrm{SU}(2)\times U(1)^2]/[\mathrm{SU}(2)\times U(1)]\), the unbroken U(1) commutes with the whole SM gauge group and therefore the only pNGB is exactly massless. Likewise, in \(\mathrm{SU}(2)^2/[\mathrm{SU}(2)\times U(1)]\) there are only two electrically charged pNGBs.

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Acknowledgements

MC would like to thank Maria Ramos for her comments and help. MC is supported by the Spanish MINECO under the Ramon y Cajal programme as well as by the Ministry of Science and Innovation under grant number FPA2016-78220-C3-3-P, and by the Junta de Andalucía grants FQM 101 and A-FQM-211-UGR18 (fondos FEDER).

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Chala, M. Review on Goldstone dark matter. Eur. Phys. J. Spec. Top. 231, 1315–1323 (2022). https://doi.org/10.1140/epjs/s11734-021-00218-6

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