⚛️ phenomenology

Coscattering Dark Matter in the Inverse Scotogenic Models

This paper proposes a viable dark matter scenario within the inverse scotogenic model where nearly degenerate dark scalars achieve the correct relic abundance through coscattering and coannihilation processes, while simultaneously satisfying constraints from lepton flavor violation, direct detection, and cosmological observations, and predicting observable displaced vertex signatures from the decay of the heavier scalar.

Original authors: Ang Liu, Zhi-Long Han, Fei Huang, Feng-Lan Shao, Wei Wang

Published 2026-06-29

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Ang Liu, Zhi-Long Han, Fei Huang, Feng-Lan Shao, Wei Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Solving Two Mysteries at Once

Imagine the universe has two big, unsolved mysteries:

Dark Matter: An invisible substance that holds galaxies together but we can't see or touch.
Tiny Neutrino Masses: Ghostly particles that pass through everything, yet somehow have a tiny bit of weight.

Scientists have a theory called the Scotogenic Model (think of it as a "Dark Matter Factory"). It suggests that these two mysteries share a common origin: the same hidden particles that create Dark Matter also generate the tiny mass of neutrinos through a complex loop process.

However, there's a problem. The standard version of this factory is under strict police surveillance. If the particles interact too strongly, we would have seen signs of them by now (like "flavor violations" or direct hits in detectors), but we haven't. The factory needs a way to produce the right amount of Dark Matter without getting caught.

The New Idea: The "Coscattering" Dance

This paper proposes a clever workaround called Coscattering.

The Analogy:
Imagine a crowded dance floor (the early universe).

The Main Character (Dark Matter, $\phi_1$ ): A shy dancer who wants to stay on the floor but is slowly leaving.
The Partner (Dark Partner, $\phi_2$ ): A slightly heavier, more energetic dancer who is very close in weight to the Main Character.
The Crowd (Standard Model particles): The other people on the dance floor.

In the old "Coannihilation" method, the Main Character and the Partner would pair up and annihilate (disappear) together to keep the numbers right. But this often leaves a trail of evidence that gets them caught by the police.

In the new Coscattering method, the Main Character doesn't disappear. Instead, they play a game of "musical chairs" with the Crowd.

The Main Character ( $\phi_1$ ) bumps into a Crowd member and swaps places with the Partner ( $\phi_2$ ).
The Partner ( $\phi_2$ ) is now on the floor, but because the Partner is slightly heavier, they are unstable. They quickly decay or swap back.
This constant swapping keeps the Main Character's population at the perfect "Goldilocks" level (the correct amount of Dark Matter we see today) without them having to annihilate in a way that leaves obvious traces.

The Two Pathways: How They Talk

The paper explores two ways these dark particles can interact with the visible world to perform this dance:

1. The Higgs Portal (The "Heavy Hitter" Connection)

How it works: The dark particles talk to the visible world through the Higgs boson (the particle that gives mass to everything else).
The Catch: To avoid being caught by "Direct Detection" experiments (which look for dark matter hitting atoms), the connection must be very weak.
The Result: The authors found that if the mass difference between the Main Character and the Partner is small (like 1 to 10 GeV), and the Partner is heavy, the Coscattering dance works perfectly.
The Signature: Because the Partner is slightly heavier, it eventually decays into the Main Character plus some visible particles. If the mass difference is just right, this decay happens slowly, creating a "Displaced Vertex."
- Analogy: Imagine a firecracker that is lit but takes a few seconds to explode. In a particle collider, this looks like a particle traveling a short distance before suddenly bursting into visible debris. This is a unique fingerprint that current and future colliders (like the LHC) can look for.

2. The Yukawa Portal (The "Lepton" Connection)

How it works: Instead of the Higgs, the dark particles talk to the visible world through leptons (electrons, muons, taus).
The Catch: This interaction is very sensitive to "Lepton Flavor Violation" (particles changing identities in forbidden ways). To avoid this, the dark particles must have a very specific "hierarchy" of connections: they must love the heavy leptons (like taus) but barely notice the light ones (like electrons).
The Result: This also allows for the Coscattering dance. The Partner ( $\phi_2$ ) decays into the Main Character plus leptons.
The Signature: Similar to the Higgs portal, if the mass difference is right, the Partner lives long enough to travel a bit before decaying, creating a Displaced Vertex signature. However, the decay products here are purely leptons (electrons/muons) rather than the mix of particles seen in the Higgs portal.

What the Paper Actually Found

The authors ran the numbers (simulations) to see if this idea holds up against all current rules:

It Works: They found specific "sweet spots" in the parameter space where Coscattering produces exactly the right amount of Dark Matter.
It Evades the Police: Because the interactions are tuned just right (weak enough to avoid direct detection, but strong enough to keep the dance going), these models survive current constraints from:
- Direct Detection: (LZ experiment)
- Indirect Detection: (Fermi-LAT, looking for dark matter collisions in space)
- Flavor Violation: (MEG experiment)
The "Long-Lived" Clue: The most exciting prediction is the Displaced Vertex. The "Partner" particle ( $\phi_2$ $ϕ_{2}$ ) is long-lived.
- If the mass difference is small (1 GeV), the Partner lives too long and disappears before it can be seen (invisible).
- If the mass difference is larger (10 GeV), the Partner decays inside the detector, leaving a visible "delayed explosion" signature.
The Future: The paper suggests that the High-Luminosity LHC (HL-LHC), a future upgrade to the world's biggest particle collider, is our best bet to find these particles. It could detect the "delayed explosion" signature if the particles are light enough.

Summary in a Nutshell

This paper proposes a new way for Dark Matter to exist without breaking the rules of physics. Instead of disappearing in a flash, Dark Matter stays in the universe by constantly swapping places with a slightly heavier "sibling" particle. This sibling is unstable and eventually decays, leaving a delayed, visible trail (a displaced vertex) that future particle colliders can hunt for. This mechanism explains both Dark Matter and neutrino masses while staying hidden from current detectors.

Technical Summary: Coscattering Dark Matter in the Inverse Scotogenic Model

Problem Statement
The Scotogenic mechanism offers a unified explanation for the origin of tiny neutrino masses and dark matter (DM) by generating neutrino masses at the loop level via dark sector particles. However, conventional Scotogenic DM scenarios face stringent constraints. If DM annihilates primarily via Yukawa portal interactions, it is heavily constrained by lepton flavor violation (LFV) observations, often requiring fine-tuned hierarchical couplings. Conversely, if DM annihilates via Higgs portal interactions, it typically induces large spin-independent scattering cross-sections with nucleons, leading to exclusion by current direct detection experiments (e.g., LZ). Furthermore, generating non-zero neutrino masses within this framework generally requires at least two generations of dark particles. The paper addresses the challenge of constructing a viable Scotogenic model that simultaneously satisfies neutrino mass constraints, avoids LFV and direct detection limits, and produces the correct relic density without excessive fine-tuning.

Methodology
The authors investigate the Inverse Scotogenic Model, which extends the Standard Model (SM) with a $Z_2$ -symmetric dark sector containing:

A fermion doublet $\Psi = (\psi^0, \psi^-)^T$ and a singlet Majorana fermion $\chi$ .
Three real scalar singlets $\phi_i$ ( $i=1, 2, 3$ ).
The lightest scalar $\phi_1$ is identified as the DM candidate.

The study focuses on the regime where the masses of the first two scalars are nearly degenerate ( $m_{\phi_1} \lesssim m_{\phi_2}$ ), while $m_{\phi_3}$ is significantly heavier. This mass hierarchy allows for coscattering processes ( $\phi_2 \text{SM} \to \phi_1 \text{SM}$ ) and coannihilation processes ( $\phi_1 \phi_2 \to \text{SM SM}$ ) to dominate the thermal freeze-out, rather than standard DM self-annihilation.

The analysis is conducted in two distinct portal scenarios:

Higgs Portal Scenario: Dominated by scalar interactions with the SM Higgs ( $\lambda_{ij} \gg y_{i\alpha}$ ). The authors solve coupled Boltzmann equations to track the evolution of abundances $Y_{\phi_1}$ and $Y_{\phi_2}$ , considering annihilation, conversion, and decay channels mediated by the Higgs.
Yukawa Portal Scenario: Dominated by interactions with dark fermions ( $y_{i\alpha} \gg \lambda_{ij}$ ). Here, annihilation and conversion occur via lepton exchange. The authors implement the Casas-Ibarra parametrization to relate Yukawa couplings to neutrino oscillation data, ensuring the model reproduces observed neutrino masses.

The parameter space is scanned to satisfy the Planck relic density constraint ( $\Omega h^2 \in [0.117, 0.123]$ ) while checking against:

Direct Detection: Constraints from LZ and projections for DARWIN.
Indirect Detection: Limits from Fermi-LAT, H.E.S.S., and CTA on annihilation cross-sections.
Flavor Physics: LFV constraints (specifically $\mu \to e\gamma$ ).
Cosmology: Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) constraints on the long-lived decay of the heavier partner $\phi_2$ .
Collider Searches: Higgs invisible decay limits (ATLAS) and signatures of long-lived particles (displaced vertices) and dilepton + missing energy at LHC and HL-LHC.

Key Contributions and Results

Viable Coscattering Regime: The paper demonstrates that coscattering ( $\phi_2 \text{SM} \to \phi_1 \text{SM}$ ) provides a viable pathway for Scotogenic DM. In the Higgs portal, this regime favors small mass splittings ( $\Delta m_\phi \lesssim 10$ GeV) and large couplings to the heavier scalar ( $\lambda_2 \sim \mathcal{O}(1)$ ). In the Yukawa portal, it requires a large coupling for the heavier scalar ( $y_2 \sim 1$ ) and a tiny coupling for the DM ( $y_1 \lesssim 10^{-4}$ ).
Relaxation of Constraints:
- Direct Detection: The coscattering mechanism allows for very small couplings to the SM Higgs ( $\lambda_1$ ) or suppressed effective cross-sections, naturally evading current LZ bounds which typically exclude scalar DM with larger couplings.
- LFV: In the Yukawa portal, the required hierarchical structure of Yukawa couplings ( $|y_{ie}| \ll |y_{i\mu}| \lesssim |y_{i\tau}|$ ) naturally satisfies LFV constraints while reproducing neutrino masses.
Phenomenology of the Dark Partner ( $\phi_2$ ):
- Long-Lived Signatures: Due to small mass splittings and suppressed couplings, $\phi_2$ is often long-lived, decaying via three-body processes ( $\phi_2 \to \phi_1 f \bar{f}$ ).
- Displaced Vertices (DV): For mass splittings $\Delta m_\phi \sim 10$ GeV, $\phi_2$ decays within the detector volume, producing observable displaced vertex signatures at the LHC. The paper identifies specific regions (e.g., $m_{\phi_2} \lesssim 400$ GeV in the Yukawa portal) where LHC and future HL-LHC can probe these signals.
- Cosmological Bounds: For small mass splittings ( $\Delta m_\phi = 1$ GeV), the long lifetime of $\phi_2$ can violate BBN constraints, effectively ruling out certain parameter regions unless the mass splitting is increased or the coupling is tuned.
Comparison of Portals:
- Higgs Portal: Dominated by hadronic decays of $\phi_2$ . Coscattering is viable for $m_{\phi_1} \lesssim 1.1$ TeV. Indirect detection constraints are weak due to suppressed annihilation cross-sections.
- Yukawa Portal: Dominated by leptonic decays of $\phi_2$ . Coscattering is viable up to $m_{\phi_1} \sim 4$ TeV. The model predicts specific dilepton signatures ( $\ell^+\ell^- + \not{E}_T$ ) from the decay of the fermion doublet $\Psi$ , which are currently constrained by LHC searches for $m_F \lesssim 660$ GeV.

Significance and Claims
The paper claims that the coscattering mechanism in the Inverse Scotogenic Model offers a robust solution to the tension between relic density, neutrino mass generation, and experimental constraints.

Naturalness: It avoids the need for extreme fine-tuning of couplings to satisfy LFV or direct detection limits, as the small couplings required for coscattering are naturally compatible with these constraints.
Testability: Unlike many "invisible" DM scenarios, this model predicts distinct, testable signatures. Specifically, the long-lived nature of the dark partner $\phi_2$ leads to displaced vertex signatures at colliders, providing a unique discovery channel distinct from standard WIMP searches.
Differentiation: The authors note that the two portal scenarios (Higgs vs. Yukawa) can be distinguished experimentally by the decay products of $\phi_2$ : hadronic final states dominate in the Higgs portal, while leptonic final states dominate in the Yukawa portal.

The study concludes that while current direct detection and indirect detection limits constrain the parameter space, the coscattering regime remains viable and is primarily testable through future collider searches for long-lived particles and displaced vertices at the LHC and HL-LHC.