Impact of conversion-driven processes on singlet-doublet Majorana dark matter relic

This paper demonstrates that assuming a Majorana nature for singlet-doublet dark matter significantly expands the viable parameter space for relic density and direct detection compared to the Dirac scenario, allowing for dark matter masses up to 1750 GeV and mixing angles up to 0.45 through the inclusion of conversion-driven processes.

The Gist

The Big Picture: The "Dark Matter" Mystery

Imagine the universe is a giant, dark room. We can see the furniture (stars and galaxies) because they reflect light, but we know there is a lot of invisible stuff filling the room that holds everything together. We call this Dark Matter.

Scientists have a theory that this invisible stuff is made of tiny particles called WIMPs (Weakly Interacting Massive Particles). The paper you shared investigates a specific "family" of these particles called the Singlet-Doublet Model.

The Characters: The "Odd Couple"

In this model, Dark Matter isn't just one lonely particle. It's a team of two different types of particles that are "cousins" to each other:

1. The Singlet: A shy, invisible particle that doesn't talk to normal matter much.
2. The Doublet: A more social particle that can interact with the forces of the universe (like electricity and magnetism).

Usually, these two are distinct. But in this model, they can mix. Think of it like two people at a party: one is wearing a mask (Singlet) and the other is not (Doublet). Sometimes, they swap masks or blend their identities. The paper studies how much they mix (called the mixing angle) and how heavy they are.

The Problem: The "Party Crashers"

In the early universe, everything was hot and crowded, like a massive, chaotic dance party. As the universe expanded and cooled, the party started to empty out.

For Dark Matter to exist in the amount we see today, the particles had to stop disappearing (annihilating) at just the right time.

• The Old Theory (Dirac): Previous studies assumed these particles were like regular matter (like electrons). They found that if the particles mixed too little, they would disappear too fast, leaving the universe empty of Dark Matter. If they mixed too much, they would disappear too slowly, leaving too much. This left a very narrow "Goldilocks zone" for the particles to exist.
• The New Theory (Majorana): This paper asks: What if these particles are their own opposites? (Like a particle that is its own antiparticle). This changes the rules of the dance.

The Discovery: A Much Bigger Dance Floor

The authors found that if these particles are "Majorana" type (their own antiparticles), the rules change significantly:

1. The "Conversion" Trick: The paper highlights a process called conversion-driven processes. Imagine the shy Singlet particle wants to leave the party, but it can't. However, it can quickly swap places with the social Doublet particle. The Doublet, being more social, runs into other particles and disappears (annihilates). This swap helps reduce the number of Singlets, keeping the total amount of Dark Matter in balance.
2. A Wider Range: Because of this "swapping" trick, the model works for a much wider variety of particle weights and mixing levels.
   • Old Limit: Particles could only weigh between 100 and 750 units.
   • New Limit: Particles can now weigh anywhere from 100 to 1,750 units.
   • Mixing: They can mix much less (or much more) than previously thought and still get the right amount of Dark Matter.

The "Thermal" vs. "Non-Thermal" Zones

The paper divides the universe into two scenarios based on how well these particles interact:

• The Thermal Zone (The Hot Party): The particles interact enough to stay in balance with the rest of the universe until the party cools down. This is the "safe zone" where the math works perfectly.
• The Non-Thermal Zone (The Cold Room): If the particles mix too little, they stop interacting early. They get "frozen out" before the party ends. In this case, the amount of Dark Matter is determined by a different, slower process (like a slow leak rather than a flood). The paper notes that even in this "frozen" state, the model can still work, but it requires very specific conditions.

The Detective Work: How Do We Find Them?

Since we can't see Dark Matter, scientists look for clues in giant particle colliders (like the LHC) and underground detectors.

1. The "Disappearing Act" (Collider Searches):

   • If the particles mix a little bit, the "Doublet" cousin might live for a tiny fraction of a second before turning into Dark Matter.
   • Analogy: Imagine a runner who sprints a few meters and then vanishes. In a particle collider, this looks like a "displaced vertex"—a spot where a particle appears to travel a short distance before decaying.
   • The Finding: The paper shows that because of the new "conversion" math, these particles might live long enough to be caught by detectors like CMS, ATLAS, or a future detector called MATHUSLA.

2. The "Ghost" Hunt (Direct Detection):

   • Scientists also try to catch Dark Matter by waiting for it to bump into atoms deep underground (like in the LZ experiment).
   • The Finding: Because these particles are "Majorana" (their own antiparticles), they don't interact with a specific force (the Z-boson) that usually makes them easy to catch. This makes them "ghostlier." Paradoxically, this is good news for the model: because they are harder to catch, the rules allow them to mix more than previously thought without being ruled out by current experiments.

The Conclusion

The paper concludes that if Dark Matter is made of these "Majorana" Singlet-Doublet particles, the universe is a much more flexible place than we thought.

• The particles can be much heavier (up to 1,750 GeV).
• They can mix in a much wider range of ways.
• The "conversion" process (swapping between the shy and social cousins) is the key that keeps the universe from having too much or too little Dark Matter.

This opens up a much larger "search area" for scientists to look for these particles in future experiments.

Technical Summary

Technical Summary: Impact of Conversion-Driven Processes on Singlet-Doublet Majorana Dark Matter Relic

Problem Statement
The paper addresses the parameter space of the Singlet-Doublet Dark Matter (SDDM) model, specifically investigating the case where the dark matter (DM) candidate is a Majorana fermion. While the SDDM model is a minimal extension of the Standard Model (SM) involving a singlet fermion and a doublet fermion, previous analyses have largely focused on the Dirac nature of the DM or have neglected "conversion-driven" processes in specific regimes. In the SDDM framework, the relic abundance is determined not only by standard annihilation and co-annihilation but also by conversion-driven processes, which include co-scattering, decay, and inverse-decay. The authors aim to determine the viable parameter space for a Majorana SDDM candidate, explicitly incorporating these conversion-driven mechanisms, and to compare the resulting constraints with those of the Dirac scenario and existing experimental bounds.

Methodology
The authors employ a thermal freeze-out framework to study the cosmological evolution of the SDDM model. The model is defined by three primary parameters: the DM mass ($M_{DM}$), the singlet-doublet mixing angle ($\sin \theta$), and the mass splitting between the singlet and doublet states ($\Delta M$).

1. Model Formulation: The Lagrangian is extended with a singlet fermion $\chi$ and a doublet fermion $\Psi$, both odd under a $Z_2$ symmetry. The neutral fermion mass matrix is diagonalized to yield three Majorana mass eigenstates ($\chi_1, \chi_2, \chi_3$), with $\chi_3$ identified as the DM candidate.
2. Boltzmann Equations: To accurately track the relic density, the authors solve coupled Boltzmann equations for the comoving number densities of two distinct sectors:
   • Sector 1: The DM component ($\chi_3$).
   • Sector 2: The remaining dark sector particles ($\chi_1, \chi_2, \psi^\pm$), which maintain chemical equilibrium among themselves via gauge interactions.
     The evolution equations include terms for annihilation ($11 \to 00$, $22 \to 00$), co-annihilation ($12 \to 00$), co-scattering ($20 \to 10$), and decay/inverse-decay ($\Gamma_{2 \to 1}$).
3. Numerical Analysis: A comprehensive numerical scan is performed over the parameter space ($10 \text{ GeV} \leq M_{DM} \leq 2000 \text{ GeV}$). The authors utilize the code micrOMEGAs to calculate relic densities, explicitly verifying thermalization conditions ($\Gamma/H > 1$). They compare scenarios with and without co-scattering contributions to isolate the impact of conversion-driven processes.
4. Experimental Constraints: The viable parameter space is constrained by:
   • Direct Detection: Limits from the LUX-ZEPLIN (LZ) experiment.
   • Collider Searches: Constraints from LEP on the doublet fermion mass and prompt search limits from ATLAS and CMS at the LHC.
   • Displaced Vertex Sensitivity: Sensitivity projections for CMS, ATLAS, and MATHUSLA regarding long-lived particles.

Key Contributions and Results

• Expanded Parameter Space for Majorana DM: The study finds that assuming a Majorana nature for the SDDM candidate significantly enlarges the allowed parameter space compared to the Dirac case.
  • Dirac Case (Reference): $100 \text{ GeV} \lesssim M_{DM} \lesssim 750 \text{ GeV}$ and $10^{-6} \lesssim \sin \theta \lesssim 0.04$ (for $\Delta M > 1 \text{ GeV}$).
  • Majorana Case (This Work): $100 \text{ GeV} \lesssim M_{DM} \lesssim 1750 \text{ GeV}$ and $2 \times 10^{-7} \lesssim \sin \theta \lesssim 0.45$ (for $\Delta M > 1 \text{ GeV}$).
• Role of Conversion-Driven Processes:
  • For large mixing angles ($\sin \theta \gtrsim 0.05$), annihilation and co-annihilation dominate, and the singlet and doublet decouple simultaneously. Co-scattering effects are negligible here.
  • For small mixing angles ($\sin \theta \lesssim 0.05$), the singlet decouples early with a larger abundance. However, conversion-driven processes (specifically decay, inverse-decay, and co-scattering) allow the singlet to convert into the doublet, which then annihilates into SM particles. This mechanism reduces the singlet abundance to the observed relic density even for very small $\sin \theta$.
  • The inclusion of co-scattering is shown to be critical for $\sin \theta \lesssim 0.05$, shifting the relic parameter space and allowing correct relic densities for points that would otherwise be overabundant.
• Direct Detection Relaxation: In the Majorana scenario, the $Z$-mediated spin-independent direct detection channel is absent. Consequently, constraints are dominated by Higgs-mediated interactions, which are weaker. This allows for significantly larger mixing angles ($\sin \theta \lesssim 0.45$) compared to the Dirac case.
• Collider Signatures: The inclusion of conversion-driven processes allows for smaller mixing angles, which results in longer decay lengths for the charged doublet fermions ($\psi^\pm$). The authors demonstrate that these decay lengths fall within the sensitivity ranges of LHC displaced vertex searches (CMS and ATLAS) and the future MATHUSLA detector. Conversely, prompt search limits from ATLAS and CMS exclude regions with $M_{DM} \lesssim 197 \text{ GeV}$ and $\sin \theta \gtrsim 10^{-3}$ where the decay length is short ($c\tau < 10^{-4} \text{ m}$).

Significance
The paper claims that the Majorana nature of the singlet-doublet dark matter, combined with a full treatment of conversion-driven processes, fundamentally alters the phenomenology of the model. The primary significance lies in the demonstration that the correct relic density can be achieved over a much broader mass range (up to 1750 GeV) and for a wider range of mixing angles (up to 0.45) than previously established for Dirac candidates. Furthermore, the work highlights that conversion-driven processes are not merely a minor correction but a dominant mechanism in the small-mixing-angle regime, effectively bridging the gap between thermal equilibrium and the observed relic density. This expanded parameter space brings the model into the sensitivity reach of current and future collider experiments, particularly those searching for displaced vertices, thereby offering new avenues for testing the SDDM hypothesis.