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Sommerfeld effect in freeze-in dark matter
High Energy Physics - Phenomenology · Submitted 22 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In summary, when considering the constraint of producing correct DM relic abundance, the inclusion of SE in the portal reaction or DS internal reaction will modify the model parameters, resulting in a band-like possible parameter space.
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The abstract, sentence by sentence
If two annihilation products of dark matter (DM) particles are non-relativistic and coupled to a light force mediator, their plane wave functions are modified due to multiple exchanges of the force mediators. This gives rise to the Sommerfeld effect (SE). We consider the attractive and repulsive force SE on the relic density in different phases of freeze-in DM. We find that in the pure freeze-in region, the attractive/repulsive force SE slightly increases/decreases DM relic density by less than $20\%$ for TeV-scale DM. In the reannihilation region, if the portal coupling $\kappa$ is sufficiently large (by comparing the portal reaction rate to the Hubble rate), DM density will reach its equilibrium, and subsequently freeze out. Compared to the case without the SE, the presence of the attractive SE leads to an enlarged cross-section. As a result, a higher equilibrium value of DM density is reached, and a lower relic density is obtained after the subsequent freeze-out. However, the repulsive SE has the opposite influence. In the dark sector (DS) freeze-out region, also known as the middle flat plateau or ``mesa'' in the phase diagram, the SE has a significant impact on DM relic abundance. In this region, the attractive SE suppresses DM relic density by simultaneously enlarging the cross-section of the portal and DS internal interaction. In contrast, the repulsive SE will have the opposite effect. Finally, in the usual freeze-out region, DM relic density is suppressed or enhanced by an enlarged or reduced cross-section of the portal, respectively, due to the presence of the attractive or repulsive SE. In summary, when considering the constraint of producing correct DM relic abundance, the inclusion of SE in the portal reaction or DS internal reaction will modify the model parameters, resulting in a band-like possible parameter space.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If two annihilation products of dark matter (DM) particles are non-relativistic and coupled to a light force mediator, their plane wave functions are modified due to multiple exchanges of the force mediators. | background 1.00 | 0.06 | 0.02 | asserted 0.95 |
| s1 | This gives rise to the Sommerfeld effect (SE). | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s2 | We consider the attractive and repulsive force SE on the relic density in different phases of freeze-in DM. | contribution 1.00 | 0.75 | 0.05 | asserted 0.60 |
| s3 | We find that in the pure freeze-in region, the attractive/repulsive force SE slightly increases/decreases DM relic density by less than $20\%$ for TeV-scale DM. | result 1.00 | 0.96 | 0.12 | asserted 1.00 |
| s4 | In the reannihilation region, if the portal coupling $\kappa$ is sufficiently large (by comparing the portal reaction rate to the Hubble rate), DM density will reach its equilibrium, and subsequently freeze out. | result 0.87 | 0.51 | 0.05 | asserted 0.73 |
| s5 | Compared to the case without the SE, the presence of the attractive SE leads to an enlarged cross-section. | result 0.89 | 0.59 | 0.07 | asserted 1.00 |
| s6 | As a result, a higher equilibrium value of DM density is reached, and a lower relic density is obtained after the subsequent freeze-out. | result 0.83 | 0.84 | 0.09 | asserted 1.00 |
| s7 | However, the repulsive SE has the opposite influence. | result 0.97 | 0.70 | 0.04 | asserted 0.99 |
| s8 | In the dark sector (DS) freeze-out region, also known as the middle flat plateau or ``mesa'' in the phase diagram, the SE has a significant impact on DM relic abundance. | result 0.94 | 0.68 | 0.08 | asserted 1.00 |
| s9 | In this region, the attractive SE suppresses DM relic density by simultaneously enlarging the cross-section of the portal and DS internal interaction. | result 0.99 | 0.87 | 0.12 | asserted 1.00 |
| s10 | In contrast, the repulsive SE will have the opposite effect. | result 0.99 | 0.78 | 0.06 | asserted 0.92 |
| s11 | Finally, in the usual freeze-out region, DM relic density is suppressed or enhanced by an enlarged or reduced cross-section of the portal, respectively, due to the presence of the attractive or repulsive SE. | result 1.00 | 0.78 | 0.15 | asserted 1.00 |
| s12 | In summary, when considering the constraint of producing correct DM relic abundance, the inclusion of SE in the portal reaction or DS internal reaction will modify the model parameters, resulting in a band-like possible parameter space. | interpretation 0.75 | 0.77 | 0.76 | asserted 0.93 |
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The paper
Original abstract
If two annihilation products of dark matter (DM) particles are non-relativistic and coupled to a light force mediator, their plane wave functions are modified due to multiple exchanges of the force mediators. This gives rise to the Sommerfeld effect (SE). We consider the attractive and repulsive force SE on the relic density in different phases of freeze-in DM. We find that in the pure freeze-in region, the attractive/repulsive force SE slightly increases/decreases DM relic density by less than $20\%$ for TeV-scale DM. In the reannihilation region, if the portal coupling $\kappa$ is sufficiently large (by comparing the portal reaction rate to the Hubble rate), DM density will reach its equilibrium, and subsequently freeze out. Compared to the case without the SE, the presence of the attractive SE leads to an enlarged cross-section. As a result, a higher equilibrium value of DM density is reached, and a lower relic density is obtained after the subsequent freeze-out. However, the repulsive SE has the opposite influence. In the dark sector (DS) freeze-out region, also known as the middle flat plateau or ``mesa'' in the phase diagram, the SE has a significant impact on DM relic abundance. In this region, the attractive SE suppresses DM relic density by simultaneously enlarging the cross-section of the portal and DS internal interaction. In contrast, the repulsive SE will have the opposite effect. Finally, in the usual freeze-out region, DM relic density is suppressed or enhanced by an enlarged or reduced cross-section of the portal, respectively, due to the presence of the attractive or repulsive SE. In summary, when considering the constraint of producing correct DM relic abundance, the inclusion of SE in the portal reaction or DS internal reaction will modify the model parameters, resulting in a band-like possible parameter space.
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How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 45 sentences without a confident label
Uses the method or tool of 7 papers
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Subsequently, the Boltzmann equation becomes: [equation] This equation can be solved by introducing an effective cross-section [ref] :
The Four Basic Ways of Creating Dark Matter Through a Portal · Thermalization of the dark sector with SE · 0.88
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Assuming that DM is generated by the $f f →χχ$ reaction and the particle $f$ has a Boltzmann-distributed phase-space distribution, the thermally averaged cross-section can be simplified as follows [ref] : [equation] where $s̃_min = max[1,(m_f/m_χ)^2]$ represents the kinematically allowed velocity, introduced to account for the forbidden case [ref] or final-state SE [ref] .
Final bound-state formation effect on dark matter annihilation · The thermal average of the SE-modified cross-section · 0.80
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Assuming that DM is generated by the $f f →χχ$ reaction and the particle $f$ has a Boltzmann-distributed phase-space distribution, the thermally averaged cross-section can be simplified as follows [ref] : [equation] where $s̃_min = max[1,(m_f/m_χ)^2]$ represents the kinematically allowed velocity, introduced to account for the forbidden case [ref] or final-state SE [ref] .
Forbidden Dark Matter · The thermal average of the SE-modified cross-section · 0.80
Uses data or values from 1 paper
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To obtain the present-day DM abundance, $Ω_χh^2 ≈0.12$ [ref] , the possible parameters space of those two models are depicted in Fig [ref] with an assumed DM mass of $1TeV$.
Planck 2018 results. VI. Cosmological parameters · $2→2$ point contact FIMP · 1.00
Cites as background 23 papers
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The Final State SE [ref] is caused by the coupling between the SM particles, which modifies the annihilation cross-section.
Final state Sommerfeld effect on dark matter relic abundance · Final State SE · 0.84
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Non-perturbative effects, such as the SE, bound-state formation, resonance effects, and co-annihilation, have been well-studied in the context of freeze-out [ref] , but they are rare in the context of freeze-in.
Bound-state formation for thermal relic dark matter and unitarity · Introduction · 0.83
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Non-perturbative effects, such as the SE, bound-state formation, resonance effects, and co-annihilation, have been well-studied in the context of freeze-out [ref] , but they are rare in the context of freeze-in.
Final bound-state formation effect on dark matter annihilation · Introduction · 0.83
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