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Vector dark matter production from catalyzed annihilation
High Energy Physics - Phenomenology · Submitted 28 Jul 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the DM with a mass $m_X\gtrsim4.5$~TeV survives in the case of a long-living catalyst.
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The abstract, sentence by sentence
We provide a simple model of vector dark matter (DM) which can realize the recently proposed freeze-out mechanism with catalyzed annihilation. In our setup, a vector DM field $X_\mu$ and a catalyst field $C_\mu$ is unified by an SU(2)$_D$ gauge symmetry. These gauge fields acquire their masses via spontaneously symmetry breaking triggered by a doublet and a real triplet scalar fields. The catalyst particle is automatically lighter than the DM since it only acquires mass from the vacuum expectation value of the doublet scalar. We also introduce a dimension-5 operator to generate a kinetic mixing term between $C_\mu$ and the U(1)$_Y$ gauge field $B_\mu$. This mixing term is naturally small due to a suppression with a high UV completion scale, and thus it allows the catalyst to decay after the DM freeze-out. We derive the annihilation cross sections of processes $X^\ast+X\to 2C$ and $3C\to X^\ast+X$ and solve the Boltzmann equations for both the DM and the catalyst. We develop the analytical approximate solutions of the equations and find them matching the numerical solutions well. Constraints from relic abundance and indirect detection of DM are considered. We find that the DM with a mass $m_X\gtrsim4.5$~TeV survives in the case of a long-living catalyst. On the other hand, if the catalyst decays during the catalyzed annihilation era, then the bound can be released. We also discuss two paradigms which can maintain the kinetic equilibrium of DM until the DM freeze-out. In both cases, the freeze-out temperature of DM is an order of magnitude higher than the original model.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We provide a simple model of vector dark matter (DM) which can realize the recently proposed freeze-out mechanism with catalyzed annihilation. | contribution 1.00 | 0.92 | 0.15 | asserted 0.60 |
| s1 | In our setup, a vector DM field $X_\mu$ and a catalyst field $C_\mu$ is unified by an SU(2)$_D$ gauge symmetry. | method 0.77 | 0.75 | 0.03 | asserted 1.00 |
| s2 | These gauge fields acquire their masses via spontaneously symmetry breaking triggered by a doublet and a real triplet scalar fields. | method 0.91 | 0.53 | 0.02 | asserted 1.00 |
| s3 | The catalyst particle is automatically lighter than the DM since it only acquires mass from the vacuum expectation value of the doublet scalar. | method 0.62 | 0.62 | 0.04 | asserted 1.00 |
| s4 | We also introduce a dimension-5 operator to generate a kinetic mixing term between $C_\mu$ and the U(1)$_Y$ gauge field $B_\mu$. | method 0.71 | 0.91 | 0.02 | asserted 1.00 |
| s5 | This mixing term is naturally small due to a suppression with a high UV completion scale, and thus it allows the catalyst to decay after the DM freeze-out. | method 0.41 | 0.49 | 0.04 | asserted 0.95 |
| s6 | We derive the annihilation cross sections of processes $X^\ast+X\to 2C$ and $3C\to X^\ast+X$ and solve the Boltzmann equations for both the DM and the catalyst. | method 0.96 | 0.97 | 0.04 | asserted 1.00 |
| s7 | We develop the analytical approximate solutions of the equations and find them matching the numerical solutions well. | method 0.43 | 0.98 | 0.04 | asserted 1.00 |
| s8 | Constraints from relic abundance and indirect detection of DM are considered. | method 0.63 | 0.80 | 0.03 | asserted 0.90 |
| s9 | We find that the DM with a mass $m_X\gtrsim4.5$~TeV survives in the case of a long-living catalyst. | result 1.00 | 0.96 | 0.44 | asserted 1.00 |
| s10 | On the other hand, if the catalyst decays during the catalyzed annihilation era, then the bound can be released. | result 0.79 | 0.80 | 0.15 | asserted 0.83 |
| s11 | We also discuss two paradigms which can maintain the kinetic equilibrium of DM until the DM freeze-out. | contribution 0.96 | 0.86 | 0.05 | asserted 0.86 |
| s12 | In both cases, the freeze-out temperature of DM is an order of magnitude higher than the original model. | result 0.98 | 0.81 | 0.11 | asserted 1.00 |
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The paper
Original abstract
We provide a simple model of vector dark matter (DM) which can realize the recently proposed freeze-out mechanism with catalyzed annihilation. In our setup, a vector DM field $X_\mu$ and a catalyst field $C_\mu$ is unified by an SU(2)$_D$ gauge symmetry. These gauge fields acquire their masses via spontaneously symmetry breaking triggered by a doublet and a real triplet scalar fields. The catalyst particle is automatically lighter than the DM since it only acquires mass from the vacuum expectation value of the doublet scalar. We also introduce a dimension-5 operator to generate a kinetic mixing term between $C_\mu$ and the U(1)$_Y$ gauge field $B_\mu$. This mixing term is naturally small due to a suppression with a high UV completion scale, and thus it allows the catalyst to decay after the DM freeze-out. We derive the annihilation cross sections of processes $X^\ast+X\to 2C$ and $3C\to X^\ast+X$ and solve the Boltzmann equations for both the DM and the catalyst. We develop the analytical approximate solutions of the equations and find them matching the numerical solutions well. Constraints from relic abundance and indirect detection of DM are considered. We find that the DM with a mass $m_X\gtrsim4.5$~TeV survives in the case of a long-living catalyst. On the other hand, if the catalyst decays during the catalyzed annihilation era, then the bound can be released. We also discuss two paradigms which can maintain the kinetic equilibrium of DM until the DM freeze-out. In both cases, the freeze-out temperature of DM is an order of magnitude higher than the original model.
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References
How the literature uses it
5 arXiv papers cite this in 14 sentences
Papers citing it · 9 sentences without a confident label
Compares with it 1 paper
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In contrast, Ref. [ref] , which is based on the limits obtained by $2DM→2SM$ channel, excludes the catalyzed annihilation vector DM from $×$ model with a mass below $∼4.4 TeV$ when $r=1.2$ (see their Fig. 4).
Constraining the Secluded and Catalyzed Annihilation Dark Matter with Fermi-LAT and Planck Data · Results · 0.96
Cites it as background 4 papers
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The simplest setup of non-abelian model is to consider a gauged $$ with some multiplet fields, such as a scalar doublet [ref] , a scalar triplet [ref] , two scalar triplets [ref] , scalar doublet and triplet [ref] , scalar and Dirac fermion doublet [ref] , scalar triplet and quintet [ref] , etc [ref] .
Hidden SU(2)_D vector dark matter with a scalar septuplet · Introduction · 0.92
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Studies of model building and DM relic density for the fermionic and vector DM have been provided in [ref] and [ref] , respectively.
Constraining the Secluded and Catalyzed Annihilation Dark Matter with Fermi-LAT and Planck Data · Dark Matter Models · 0.94
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The most studied scenario is that of a scalar portal [ref] , but also models involving a pseudo-scalar [ref] , a fermion [ref] or a vector [ref] have been considered.
Complex Dark Photon Dark Matter EFT · Introduction · 0.99
What it cites · 12 sentences without a confident label
Uses the method or tool of 5 papers
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Once the amplitude is written down, the corresponding annihilation cross section can be computed in the non-relativistic limit by using the formula (E4) in Ref. [ref] [In our definition, the annihilation cross section is $1/S_i$ times of the one defined in Ref. [ref] , where $S_i=n_i$ is a symmetry factor from identical initial particles], and the result is given by ⟨σ_3v^2⟩ ≈ 1/6g_D^6/192πm_Z'^5(1-4/9r_XZ')^1/2f(r_XZ'), f(r_XZ') = 729/256r_XZ'^-6-243/16r_XZ'^-5+675/16r_XZ'^-4+1285/8r_XZ'^-3-1007/4r_XZ'^-2+2585/4r_XZ'^-1 -2317/4+415r_XZ'-12r_XZ'^2-48r_XZ'^3.
Enabling Forbidden Dark Matter · Annihilation cross sections and decay width · 0.95
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Using the formula given in Ref. [ref] , the mixing parameter is s_ϵ∼g_Dg'/6π^2(y_3v_3/m_Ψ) .
Direct detection of vector dark matter through electromagnetic multipoles · Dimension-5 effective operator · 0.81
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It can be done by the following transformation of basis [ref] : [ B_μ; C_μ ]= [ 1 -t_ϵ; 0 1/c_ϵ ] [ B̂_μ; Ĉ_μ ] , where $s_ϵ≡2cv_3/Λ$.
Direct detection of dark matter in models with a light Z' · Dimension-5 effective operator · 0.96
Uses data or values from 2 papers
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We solve the Boltzmann equations numerically for two different benchmark models: * $m_X=1$ TeV, $r_XZ'^1/2=m_X/m_Z'=1.32$, $g_D=1.015$, $t_ϵ=10^-11$, $ξ_X=ξ_Z'=10^-5$ (magenta lines of left panel in FIG.[ref]), * $m_X=6$ TeV, $r_XZ'^1/2=m_X/m_Z'=1.25$, $g_D=2.55$, $t_ϵ=10^-11$, $ξ_X=ξ_Z'=10^-5$ (blue lines of left panel in FIG.[ref]), which can reproduce the observed relic abundance of DM $Ω_X h^2≈0.12$ [ref] .
Planck 2018 results. VI. Cosmological parameters · The Boltzmann equations and the solutions · 0.89
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In the case with $m_X=1$ TeV, current direct detection bound on the magnetic moment of DM is about [ref] |μ_X/μ_N|≲10^-5, where $μ_N=e/2m_p$ is the proton magnetic moment.
Direct detection of vector dark matter through electromagnetic multipoles · The Boltzmann equations and the solutions · 0.93
Compares with 5 papers
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Comparing with the situation of Strongly Interacting Massive Particles (SIMPs) models and their variations [ref] , the depletion efficiency of DMs in the catalyzed annihilation scenario is much slower, and thus the freeze-out temperature is lower.
The SIMP Miracle · Introduction · 0.91
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Comparing with the situation of Strongly Interacting Massive Particles (SIMPs) models and their variations [ref] , the depletion efficiency of DMs in the catalyzed annihilation scenario is much slower, and thus the freeze-out temperature is lower.
The SIMPlest Miracle · Introduction · 0.91
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Comparing with the situation of Strongly Interacting Massive Particles (SIMPs) models and their variations [ref] , the depletion efficiency of DMs in the catalyzed annihilation scenario is much slower, and thus the freeze-out temperature is lower.
$Z_2$ SIMP Dark Matter · Introduction · 0.91
Cites as background 29 papers
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Vector dark matter models has been discussed in many previous studies, such as a U(1) gauge symmetry extension [ref] , a non-abelian gauge symmetry extension [ref] and a model with non-gauge field vector bosons [ref] .
Minimal Spin-one Isotriplet Dark Matter · Introduction · 0.99
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Vector dark matter models has been discussed in many previous studies, such as a U(1) gauge symmetry extension [ref] , a non-abelian gauge symmetry extension [ref] and a model with non-gauge field vector bosons [ref] .
$SU(2)_X$ Vector DM and Galactic Center Gamma-Ray Excess · Introduction · 0.99
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Vector dark matter models has been discussed in many previous studies, such as a U(1) gauge symmetry extension [ref] , a non-abelian gauge symmetry extension [ref] and a model with non-gauge field vector bosons [ref] .
The Higgs-portal for vector Dark Matter and the Effective Field Theory approach: a reappraisal · Introduction · 0.99
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