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Dark Matter Bound State Formation in Fermionic $Z_2$ DM model with Light Dark Photon and Dark Higgs Boson
High Energy Physics - Phenomenology · Submitted 10 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The emissions of a longitudinal vector boson (or somehow equivalently a Goldstone boson) during the DM bound state formations are crucial to induce a significant reannihilation process, reducing the dark matter relic abundance.
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The abstract, sentence by sentence
If fermionic dark matter (DM) is stabilized by dark $U(1)$ gauge symmetry that is spontaneously broken into its subgroup $Z_2$, the particle contents of the model becomes very rich: DM and excited DM, both of them are Majorana fermions, as well as two dark force mediators, dark photon and dark Higgs boson are naturally present due to the underlying dark gauge symmetry. In this paper, we study the DM bound state formation processes within this scenario, assuming both dark photon and dark Higgs are light mediators and including the effects of excited DM. The Goldstone boson contributions to the potential matrix in the Schr\"{o}dinger equations are found to be important. The emissions of a longitudinal vector boson (or somehow equivalently a Goldstone boson) during the DM bound state formations are crucial to induce a significant reannihilation process, reducing the dark matter relic abundance. Most of the stringent constraints for this kind of dark matter considered in the literature are simply evaded.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If fermionic dark matter (DM) is stabilized by dark $U(1)$ gauge symmetry that is spontaneously broken into its subgroup $Z_2$, the particle contents of the model becomes very rich: DM and excited DM, both of them are Majorana fermions, as well as two dark force mediators, dark photon and dark Higgs boson are naturally present due to the underlying dark gauge symmetry. | background 1.00 | 0.06 | 0.03 | asserted 0.97 |
| s1 | In this paper, we study the DM bound state formation processes within this scenario, assuming both dark photon and dark Higgs are light mediators and including the effects of excited DM. | contribution 0.99 | 0.85 | 0.05 | asserted 0.86 |
| s2 | The Goldstone boson contributions to the potential matrix in the Schr\"{o}dinger equations are found to be important. | result 0.98 | 0.93 | 0.08 | asserted 1.00 |
| s3 | The emissions of a longitudinal vector boson (or somehow equivalently a Goldstone boson) during the DM bound state formations are crucial to induce a significant reannihilation process, reducing the dark matter relic abundance. | result 0.82 | 0.73 | 0.56 | asserted 1.00 |
| s4 | Most of the stringent constraints for this kind of dark matter considered in the literature are simply evaded. | result 0.75 | 0.45 | 0.18 | asserted 1.00 |
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The paper
Original abstract
If fermionic dark matter (DM) is stabilized by dark $U(1)$ gauge symmetry that is spontaneously broken into its subgroup $Z_2$, the particle contents of the model becomes very rich: DM and excited DM, both of them are Majorana fermions, as well as two dark force mediators, dark photon and dark Higgs boson are naturally present due to the underlying dark gauge symmetry. In this paper, we study the DM bound state formation processes within this scenario, assuming both dark photon and dark Higgs are light mediators and including the effects of excited DM. The Goldstone boson contributions to the potential matrix in the Schr\"{o}dinger equations are found to be important. The emissions of a longitudinal vector boson (or somehow equivalently a Goldstone boson) during the DM bound state formations are crucial to induce a significant reannihilation process, reducing the dark matter relic abundance. Most of the stringent constraints for this kind of dark matter considered in the literature are simply evaded.
Human review
References
How the literature uses it
23 arXiv papers cite this in 34 sentences
Papers citing it · 23 sentences without a confident label
Compares with it 1 paper
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[ref] and the present work find that transitions proportional to the overlap of the incoming and outgoing wavefunctions without any momentum suppression, result in the recoupling of the DM depletion processes at late times.
Dark matter bound state formation via emission of a charged scalar · Conclusion · 0.96
Cites it as support 1 paper
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* Radiative transitions between states of different Coulomb(-like) potentials, e.g. bound-state formation with emission of a charged scalar [ref] or a non-Abelian gauge boson [ref] , exhibit non-monotonic dependence on the incoming momentum, with peaks that can violate unitarity for a finite velocity range, even for fairly small values of the couplings.
Unitarity in the non-relativistic regime and implications for dark matter · Unitarity violation · 0.96
Cites it as background 8 papers
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Local $Z_2$ scalar [ref] and fermion DM models [ref] have been studied by authors for the $O(100)$ GeV – O(1) TeV WIMP scenarios.
XENON1T excess in local $Z_2$ DM models with light dark sector · Introduction · 0.91
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The inelastic (or excited) DM models with extra $U(1)_D$ gauge symmetry [ref] is one of the most popular dark sector models with light DM candidates[ In Ref. [ref] , the $U(1)_D$ symmetry is explicitly and softly broken by a dim–2 operator for scalar DM, and there is no dark Higgs boson there.
Exploring properties of long-lived particles in inelastic dark matter models at Belle II · Introduction · 0.83
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Depending on the model, bound states may form, get ionised and transition between each other radiatively [ref] , via scattering on the relativistic plasma [ref] or other re-arrangement processes [ref] .
Saha equilibrium for metastable bound states and dark matter freeze-out · Introduction · 0.94
What it cites · 79 sentences without a confident label
Builds on 2 papers
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One can directly follow the processes to derive (5.21), (5.54) in Ref. [ref] , and just extend all the wave functions in two-component case to acquire the transition amplitudes for the bound state formation.
Dark-matter bound states from Feynman diagrams · Calculation of Bound State Formation Cross Section · 0.86
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Although Ref. [ref] did not consider the multi-component wave functions, we can just extend the “overlap” integrals $ℐ$, $𝒥⃗$ and $𝒦$ in the (2.7a-c) of Ref. [ref] to the two-component case rather than deriving them starting from the Dyson-Schwinger equations.
Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential · Calculation of Bound State Formation Cross Section · 0.98
Uses the method or tool of 9 papers
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Following Ref. [ref] and expanding $e^-i b⃗ ·r⃗$ into partial waves, we acquire the following overlap integrals for the lowest orders in the “spherical Bessel function indices” [equation] where $ℐ^t_…$ indicates the corresponding partial wave expansions for all the overlap integrals, ([ref])–([ref]), with the upper symbol $t$ being either empty or $±$.
Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential · Calculation of Bound State Formation Cross Section · 0.98
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Our discussions and derivations are based on the symbols in Ref. [ref] .
Dark-matter bound states from Feynman diagrams · Calculation of Bound State Formation Cross Section · 0.93
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Also based upon the steps listed in Ref. [ref] , we define [equation] where $⟨Γ⟩_X$ and $⟨Γ⟩_X ,dis$ are the thermal averaged decay width and the dissociation rate of the bound state, respectively.
Gluino Coannihilation Revisited · Boltzmann Equations · 0.97
Uses data or values from 3 papers
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We just estimate the bounds $Γ_h →R R +Γ_h →γ^' γ^' ≲Γ_h_SM = 4.07 MeV$ (For the standard model Higgs widths, one can see the reviews in Ref. [ref] , which requires $λ_ΦH ≲2 ×10^-2$.
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties · Constraints from the Experiments · 0.92
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We just estimate the bounds $Γ_h →R R +Γ_h →γ^' γ^' ≲Γ_h_SM = 4.07 MeV$ (For the standard model Higgs widths, one can see the reviews in Ref. [ref] , which requires $λ_ΦH ≲2 ×10^-2$.
Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables · Constraints from the Experiments · 0.92
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We just estimate the bounds $Γ_h →R R +Γ_h →γ^' γ^' ≲Γ_h_SM = 4.07 MeV$ (For the standard model Higgs widths, one can see the reviews in Ref. [ref] , which requires $λ_ΦH ≲2 ×10^-2$.
Handbook of LHC Higgs Cross Sections: 2. Differential Distributions · Constraints from the Experiments · 0.92
Compares with 8 papers
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Compared with the (B.4d) in Ref. [ref] , we also have a $y^2/Q_Φ^2 g^2<1$ factor, which is usually smaller than 1 to evade the CMB recombination bound described in ([ref]), giving an extra suppression.
Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter · Reasons for Neglecting the Emission From the Mediators · 0.97
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Together with the situation of the dark Higgs boson emission, these processes are controlled by the wave function “overlap” $ℐ$, and its zeroth order expansion is no longer zero in our case, unlike in Refs. [ref] .
Dark-matter bound states from Feynman diagrams · Introduction · 0.92
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Together with the situation of the dark Higgs boson emission, these processes are controlled by the wave function “overlap” $ℐ$, and its zeroth order expansion is no longer zero in our case, unlike in Refs. [ref] .
Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential · Introduction · 0.92
Cites as background 68 papers
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Many of the models are built and calculated [See Ref. [ref] for the references on the early dark matter bound state models therein].
Dark-matter bound states from Feynman diagrams · Introduction · 0.96
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Ref. [ref] are the recent papers which had built or calculated the dark matter models in which bound state can be formed.
Stop Coannihilation in the CMSSM and SubGUT Models · Introduction · 0.87
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Ref. [ref] are the recent papers which had built or calculated the dark matter models in which bound state can be formed.
Directional detection of dark matter in universal bound states · Introduction · 0.87
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