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Anatomy of singlet-doublet dark matter relic: annihilation, co-annihilation, co-scattering, and freeze-in

Partha Kumar Paul, Sujit Kumar Sahoo, Narendra Sahu

TL;DR

This study comprehensively analyzes the singlet–doublet vector-like fermion dark matter model (SDDM) across annihilation, co-annihilation, co-scattering, freeze-in, and SuperWIMP production. It demonstrates that the common assumption of simultaneous decoupling of singlet and doublet sectors holds only for larger mixing angles $\sin\theta$, and that co-scattering and conversion-driven processes play crucial roles at small $\sin\theta$, reshaping the viable relic-density parameter space. The authors establish that including co-scattering not only enables the correct relic in previously excluded regions but also shifts viable models toward collider-sensitive regimes, notably enhancing displaced-vertex signatures at the LHC and MATHUSLA. They also delineate non-thermal production channels, with freeze-in and SuperWIMP mechanisms broadening the phenomenological landscape under stringent direct-detection and BBN constraints. Overall, the work provides a unified framework linking early-un Universe freeze-out, non-thermal production, and collider phenomenology for SDDM, with clear implications for upcoming searches.

Abstract

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle ($\sinθ$). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle $\sinθ<0.05$. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, non-thermal productions via the freeze-in and SuperWIMP mechanism are also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

Anatomy of singlet-doublet dark matter relic: annihilation, co-annihilation, co-scattering, and freeze-in

TL;DR

This study comprehensively analyzes the singlet–doublet vector-like fermion dark matter model (SDDM) across annihilation, co-annihilation, co-scattering, freeze-in, and SuperWIMP production. It demonstrates that the common assumption of simultaneous decoupling of singlet and doublet sectors holds only for larger mixing angles , and that co-scattering and conversion-driven processes play crucial roles at small , reshaping the viable relic-density parameter space. The authors establish that including co-scattering not only enables the correct relic in previously excluded regions but also shifts viable models toward collider-sensitive regimes, notably enhancing displaced-vertex signatures at the LHC and MATHUSLA. They also delineate non-thermal production channels, with freeze-in and SuperWIMP mechanisms broadening the phenomenological landscape under stringent direct-detection and BBN constraints. Overall, the work provides a unified framework linking early-un Universe freeze-out, non-thermal production, and collider phenomenology for SDDM, with clear implications for upcoming searches.

Abstract

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle . We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, non-thermal productions via the freeze-in and SuperWIMP mechanism are also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

Paper Structure

This paper contains 18 sections, 25 equations, 22 figures, 1 table.

Table of Contents

  1. Introduction
  2. The singlet-doublet dark matter model
  3. Dark matter phenomenology
  4. Thermal production of dark matter
  5. Thermal DM relic in the large mixing regime via annihilation and co-annihilation
  6. Thermal dark matter relic via the conversion-driven processes in the small $\sin\theta$ regime
  7. Dark matter production via freeze-in mechanism
  8. Dark matter production via SuperWIMP mechanism
  9. Direct detection of dark matter
  10. Displaced vertex signatures
  11. Conclusions
  12. Evolution of abundances for point $A$ in Table \ref{['tab:tab1']}
  13. Feynman Diagrams of the processes involved in relic density
  14. Annihilation of dark matter
  15. Annihilation and co-annihilation among the sector 2 particles
  16. ...and 3 more sections

Figures (22)

  • Figure 1: Allowed parameter space of DM for which DM is in equilibrium with SM bath and the $\mathcal{Z}_2$-odd doublet. All the points in the plots (left and right) satisfy the required relic density. The grey-shaded region in both the plots shows the LEP bound DELPHI:2003uqw on the heavy fermion doublet.
  • Figure 2: Left: Evolutions of sector 1 and sector 2 particle abundances for $M_{\rm DM}$=146.48 GeV, $\Delta M=10.5$ GeV, and $\sin\theta=1.19\times10^{-1}$ are shown for correct DM relic density $\Omega_{\rm DM}h^2\simeq0.12$. Right: The comparison of the interaction rates w.r.t Hubble is shown as a function of temperature for the parameters given in the left panel.
  • Figure 3: Left: Evolutions of sector 1 and sector 2 particle abundances for $M_{\rm DM}$=146.48 GeV, $\Delta{M}=8.4$ GeV, and $\sin\theta=1.19\times10^{-5}$ are shown for correct DM relic density $\Omega_{\rm DM}h^2\simeq0.12$. Right: The comparison of the interaction rates w.r.t Hubble is shown as a function of temperature for the parameters given in the left panel.
  • Figure 4: Variation of DM relic density w.r.t. DM mass with the fixed mass splitting of $1~\rm GeV\le\Delta{M}\le5$ GeV for $10^{-2}\le\sin\theta\le10^{-1}$ [ left] and $10^{-5}\le\sin\theta\le10^{-4}$ [ right]. For the blue colored points, we have solved Eqs. (\ref{['eq:Y1']}) and (\ref{['eq:Y2']}), by switching off the co-scattering processes, while for the red points we have considered all the processes given in Eqs. (\ref{['eq:Y1']}) and (\ref{['eq:Y2']}).
  • Figure 5: Variation of DM relic density w.r.t DM mass with the fixed mass splitting of $5~{\rm GeV}\le\Delta{M}\le10$ GeV for $10^{-2}\le\sin\theta\le10^{-1}$ [ left] and $10^{-5}\le\sin\theta\le10^{-4}$ [ right]. For the blue colored points, we have solved Eqs. (\ref{['eq:Y1']}) and (\ref{['eq:Y2']}), by switching off the co-scattering processes, while for the red points we have considered all the processes given in Eqs. (\ref{['eq:Y1']}) and (\ref{['eq:Y2']}).
  • ...and 17 more figures