Sub-GeV Dark Matter as Pseudo-Nambu-Goldstone Bosons from the Seesaw Scale

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Sub-GeV Dark Matter as Pseudo-Nambu-Goldstone Bosons from the Seesaw Scale

Michele Frigerio, Thomas Hambye, and Eduard Masso

Phys. Rev. X 1, 021026 – Published 29 December 2011

Abstract

Pseudo-Nambu-Goldstone bosons (pNGBs) are naturally light, spin-zero particles that can be interesting dark-matter (DM) candidates. We study the phenomenology of a pNGB $θ$ associated with an approximate symmetry of the neutrino seesaw sector. A small coupling of $θ$ to the Higgs boson is induced radiatively by the neutrino Yukawa couplings. By virtue of this Higgs-portal interaction, (i) the pNGB acquires a mass $m_{θ}$ proportional to the electroweak scale, and (ii) the observed DM relic density can be generated by the freeze-in of $θ$ particles with mass $m_{θ} ≃ 3 MeV$ . Alternatively, the coupling of $θ$ to heavy sterile neutrinos can account for the DM relic density, in the window 1 keV $≲ m_{θ} ≲ 3 MeV$ . The decays of $θ$ into light fermions are suppressed by the seesaw scale, making such pNGBs sufficiently stable to play the role of DM.

Received 5 August 2011

DOI:https://doi.org/10.1103/PhysRevX.1.021026

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Michele Frigerio^1,2,3,*, Thomas Hambye^4,†, and Eduard Masso⁵

¹CNRS, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier, France,
²Université Montpellier 2, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier, France
³Institut de Física d’Altes Energies, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
⁴Service de Physique Théorique, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
⁵Grup de Física Teòrica, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

^*frigerio@ifae.es
^†thambye@ulb.ac.be

Popular Summary

Baryonic visible matter makes up less than 5% of the matter of the Universe. The remaining part can be accounted for by dark matter and dark energy that are not directly visible. The dark matter is about five times more abundant than the baryonic matter. Its existence has been firmly established on the grounds of its gravitational effects, but we do not know the basic properties of the dark-matter particles: mass, spin, couplings to other particles. In this paper we propose a new candidate for the dark matter particles: A pseudo Nambu-Goldstone boson–a naturally light spinless particle, which arises from the spontaneous breaking of a global symmetry of the theory.

The proposed dark-matter candidate has a number of appealing properties: (i) Its mass is induced by an energy scale already present in the visible sector, and the dark-matter density at present is determined by the same couplings that generate its mass; (ii) it is stable on cosmological time scales, because its decays to the visible sector are suppressed by the large energy scale of spontaneous symmetry breaking.

We propose a concrete realization of our dark-matter scenario, which is closely related to the origin of light neutrino masses. The dark matter and the Higgs boson, responsible for the electroweak symmetry breaking, are very weakly coupled via neutrino interactions. As a consequence, the dark-matter mass is connected to the electroweak scale in a natural way, and its decays are suppressed by the smallness of the neutrino masses.

In our proposed scenario, we find that the correct dark-matter density is generated by the annihilation of heavy neutrinos and Higgs bosons, as long as the dark-matter mass lies in the range from keV to MeV. We also find that the late decays today of dark matter into light neutrinos and electrons produce a flux that could be observed in cosmological and astrophysical measurements.

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Issue

Vol. 1, Iss. 2 — October - December 2011

Subject Areas

Particles and Fields

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Images

Figure 1
The pNGB coupling to the sterile neutrino, $g$ , versus the pNGB mass, $m_{θ}$ , in GeV. We have fixed $m_{ν} = 0.05 eV$ and $k = 1$ . The upper (lower) green shaded region is excluded by requiring the SSB scale $f$ to be larger than 1 TeV (smaller than the Planck scale). The four dotted lines correspond to these constant values of the sterile-neutrino mass, from top to bottom: $m_{N} = 10^{2}$ , $10^{6}$ , $10^{10}$ , $10^{14} GeV$ . The thin diagonal (vertical) line indicates the lower value of $g$ ( $m_{θ}$ ) that leads to a thermalization of $θ$ . The thick curving line corresponds to a $θ$ relic density equal to the observed DM relic density, as follows from the numerical solution of the Boltzmann equation (for $m_{h} = 120 GeV$ ). Since $θ$ is produced by freeze-in, its relic density grows with its couplings $g$ and $λ = m_{θ}^{2} / v^{2}$ ; therefore, the region below and to the left (above and to the right) of the thick curving line corresponds to $Ω_{θ} < Ω_{DM} (> Ω_{DM})$ .Reuse & Permissions
Figure 2
The decay thermalization rate, $γ_{D h} / (n_{θ}^{eq} H)$ (black curve), compared to the various scattering thermalization rates, $γ_{annih}^{a} / (n_{θ}^{eq} H)$ for $a = W$ , $Z$ , $h$ , $t$ , $b$ ( the red, blue, green, orange and purple curves, respectively), as a function of $z = m_{h} / T$ and for $m_{h} = 120 GeV$ , $m_{θ} = 2.8 MeV$ . For freeze-in these rates remain always well below 1, which is the thermalization value.Reuse & Permissions
Figure 3
The constraints on the DM lifetime in the $m_{θ} − g$ plane, for $m_{ν} = 0.05 eV$ . The thick black curve, corresponding to the correct DM relic density, as well as the dotted vertical lines, corresponding to constant values of $m_{N}$ , are the same as presented in Fig. 1. The curve is dashed for $m_{θ} ≲ 1 keV$ , because DM is warm in this region (see the text), and for $g ≲ 10^{- 5}$ , because of the theoretical bound $f < M_{P}$ , shown in Fig. 1. The blue solid (dashed) line is the upper bound on $g$ from DM decays into neutrinos coming from astrophysics and cosmology (from the Universe lifetime); the blue shaded region is therefore excluded. The red solid line is the analog bound for DM decays into $e^{+} e^{-}$ ; the red shaded region is correspondingly excluded. Finally, the brown dash-dotted line is a conservative estimate of the upper bound on $g$ from DM decays into photons (see the text).Reuse & Permissions
Figure 4
The same as in Fig. 3, but for a heavier-neutrino-mass scale, $m_{ν} = 1 eV$ . The extra red dashed line is the upper bound from $1 / Γ (θ \to e^{+} e^{-}) > τ_{0}$ . (In the case of Fig. 3, the analog line lies entirely in the region $g > 1$ and $m_{θ} > 1 GeV$ , which is not displayed.)Reuse & Permissions

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