Light fermionic dark matter window in the scotogenic inverse seesaw model

This paper identifies a viable light fermionic dark matter candidate with a mass between 58 and 63 GeV within the scotogenic inverse seesaw model that simultaneously explains neutrino masses and satisfies all current experimental constraints, while remaining testable by next-generation direct detection experiments and future colliders.

The Gist

Imagine the universe is a giant, locked puzzle box. For decades, physicists have been trying to solve two of the biggest mysteries inside it: Why do tiny particles called neutrinos have mass? and What is "Dark Matter," the invisible stuff that holds galaxies together?

Usually, scientists try to solve these two problems with two different keys. But in this paper, a team of researchers from South China Normal University suggests a "Master Key" that opens both locks at once. They are using a theoretical framework called the Scotogenic Inverse Seesaw Model.

Here is the story of their discovery, explained without the heavy math.

1. The Setup: A Secret Society of Particles

Think of the Standard Model (our current best theory of physics) as a bustling city with known citizens (electrons, quarks, etc.). But this city has a secret underground society.

The researchers propose a new "neighborhood" in this city populated by three types of invisible, "Z2-odd" particles (a fancy way of saying they are hidden from normal view):

• Heavy Neighbors: A heavy vector-like lepton and some heavy scalar fields.
• The Dark Matter Candidate: A light, neutral fermion (let's call him Mr. Dark).

Because of a special rule in this neighborhood (the $Z_2$ symmetry), Mr. Dark cannot decay into anything else. He is immortal. This makes him the perfect candidate for Dark Matter.

2. The Magic Trick: How Neutrinos Get Mass

In this model, neutrinos are like shy ghosts. They don't have mass on their own. But, they can borrow mass through a "loop" of interactions with the heavy neighbors.

Imagine a neutrino trying to cross a river. It can't swim, so it hops on a boat (the heavy particles). As it travels, it interacts with the boat's engine (the Higgs field), and by the time it gets to the other side, it has gained a little weight (mass). This happens in a loop, which is why it's called a "scotogenic" (dark-origin) model.

3. The Great Filter: Finding the "Goldilocks" Zone

The team ran millions of computer simulations to see if this model works in the real world. They had to pass a series of strict "security checks" (experimental constraints):

• The Flavor Police: Did Mr. Dark cause muons to turn into electrons too often? (No, the data says no).
• The Invisible Decay Police: Did the Higgs or Z bosons disappear into Mr. Dark too often? (No, the data says no).
• The Density Police: Is there enough Mr. Dark left over from the Big Bang to explain the universe? (Yes, but only if he has a very specific weight).

The Result: They found a tiny, narrow window where Mr. Dark can exist without breaking any laws.

• The Weight: Mr. Dark must weigh between 58 and 63 GeV.
• The Analogy: Imagine trying to fit a suitcase into an overhead bin. If it's too small, it rattles around (too little mass). If it's too big, it won't fit (too much mass). Mr. Dark is the perfect size to fit exactly into the "Higgs Resonance" slot. He is just under half the weight of the Higgs boson, which allows him to be produced efficiently in the early universe but not so efficiently that he wipes out all the other matter.

4. The Hunt: How Do We Catch Him?

The paper explains how we can catch Mr. Dark using two different methods:

Method A: The "Silent" Hunt (Direct Detection)

Imagine Mr. Dark is walking through a crowd of people (atomic nuclei in a detector).

• The Spin Problem: Because Mr. Dark is a "Majorana" particle (he is his own antiparticle), he is very shy when it comes to "Spin-Independent" interactions (pushing against the crowd). He barely nudges them.
• The Spin-Dependent Nudge: However, he is good at "Spin-Dependent" interactions (twisting the crowd).
• The Catch: Current detectors (like XENON and PandaX) are looking for the "nudge." The paper predicts that Mr. Dark is so shy that current detectors might miss him, but next-generation detectors (like PandaX-xT) will be sensitive enough to feel his subtle twist. If they don't find him, this whole theory is dead.

Method B: The "Collider" Hunt (ILC)

Imagine smashing two high-speed trains (electrons and positrons) together at the International Linear Collider (ILC).

• The Signal: When they crash, they might produce a pair of Mr. Dark particles. Since Mr. Dark is invisible, he flies away, taking energy with him.
• The Clue: We won't see Mr. Dark, but we will see two visible leptons (like electrons or muons) flying out in a specific pattern, leaving a "hole" in the energy balance (Missing Energy).
• The Sweet Spot: The team found that if Mr. Dark weighs between 58.7 and 59.3 GeV, the collider can spot him with high confidence (about 2.5 sigma, which is a "strong hint" in physics).

The Big Picture

This paper is like finding a specific address in a massive city.

1. The Theory: They built a house (the model) that explains why neutrinos have mass and what Dark Matter is.
2. The Filter: They checked the house against all known laws of physics and found only one room is habitable: a tiny mass range of 58–63 GeV.
3. The Future: They handed the police (experimentalists) a map.
   • Direct Detection: "Look for a subtle twist in your detectors in the next few years."
   • Colliders: "Smash particles together at the ILC, and if you see two leptons with missing energy in this specific weight range, you've found him."

If these experiments find Mr. Dark in this specific weight range, we solve two of the universe's biggest mysteries at once. If they don't, we have to go back to the drawing board and build a new house.

Technical Summary

1. Problem Statement

The paper addresses two fundamental unresolved issues in particle physics: the origin of tiny neutrino masses and the nature of Dark Matter (DM). While the Standard Model (SM) cannot explain either, the scotogenic inverse seesaw model offers a unified framework.

• The Model: This model extends the SM by introducing a $Z_2$-odd sector containing a vector-like lepton doublet ($E$), a Majorana singlet fermion ($N$), and three real scalar singlets ($\phi_i$).
• The Gap: Previous studies on this model have largely focused on scalar DM candidates or fermionic DM with specific, restrictive assumptions about Yukawa couplings (e.g., equal left- and right-handed couplings). There is a lack of comprehensive analysis regarding light fermionic DM candidates where Yukawa couplings are scanned generally within perturbativity limits, specifically investigating the interplay between neutrino mass generation, flavor constraints, and direct detection limits.

2. Methodology

The authors employ a rigorous phenomenological approach combining analytical calculations with numerical scans:

• Model Setup:
  • Neutrino masses are generated at the one-loop level via the exchange of new scalars and fermions.
  • The lightest $Z_2$-odd neutral fermion ($\chi_3$, denoted as $\chi$) is identified as the DM candidate.
  • The Casas-Ibarra parameterization is used to express the new Yukawa coupling matrix ($y_\phi$) in terms of neutrino oscillation parameters, assuming Normal Ordering (NO) and fixing the lightest neutrino mass to 0.01 eV.
• Constraints Applied:
  • Neutrino Oscillations: Used as input to fix $y_\phi$.
  • Charged Lepton Flavor Violation (CLFV): Specifically the branching ratio $B(\mu \to e\gamma)$. The paper notes that $\mu \to 3e$ and $\mu-e$ conversion are suppressed in this fermionic scenario compared to scalar scenarios.
  • Invisible Decays: Constraints on $B(h \to \text{inv.})$ and $B(Z \to \text{inv.})$.
  • Relic Density: The thermal freeze-out mechanism is calculated using the MadDM package, requiring $\Omega_{DM}h^2 \in [0.115, 0.125]$.
  • Direct Detection: Calculation of Spin-Independent (SI) and Spin-Dependent (SD) DM-nucleon scattering cross-sections.
• Numerical Scan:
  • Approximately $1.5 \times 10^6$ parameter points were generated for $\{m_E, m_N, y_1, y_2\}$ within perturbative ranges.
  • Scalar masses were fixed to reduce dimensionality ($m_{\phi_1}=1000, m_{\phi_2}=1200, m_{\phi_3}=1400$ GeV).
  • Points were filtered against all experimental constraints.
• Collider Simulation:
  • The model was implemented in FeynRules and simulated using MadGraph5_aMC@NLO and MadAnalysis5.
  • Focus was placed on the International Linear Collider (ILC) at $\sqrt{s} = 1$ TeV, analyzing the di-lepton plus missing energy channel ($e^+e^- \to \ell^+\ell^- \chi\chi$) and mono-photon channel.

3. Key Contributions & Findings

A. The "Light Fermionic DM Window"

The most significant result is the identification of a narrow, viable mass window for the fermionic DM candidate:
$$58 \text{ GeV} \lesssim m_\chi \lesssim 63 \text{ GeV}$$
This window corresponds to the Higgs resonance funnel ($m_\chi \approx M_h/2$).

• Exclusion of Other Regions:
  • The Z-boson resonance region ($m_\chi \approx M_Z/2 \approx 45.5$ GeV) and the high-mass region ($m_\chi > 180$ GeV) are excluded by current Spin-Dependent (SD) direct detection limits (specifically from the LZ experiment).
  • In these excluded regions, the SD cross-section is dominant because the Majorana nature of the DM suppresses the Spin-Independent (SI) vector-current interactions.

B. Direct Detection Characteristics

• SI vs. SD Suppression: Due to the Majorana nature of $\chi$, SI interactions (mediated by the Higgs) are suppressed by at least four orders of magnitude compared to SD interactions (mediated by the Z boson).
• Future Sensitivity: While current experiments (LZ, PandaX-4T, XENONnT) have ruled out the Z-resonance and high-mass regions, the Higgs resonance window ($58-63$ GeV) remains viable.
• Testability: The authors demonstrate that next-generation ton-scale experiments, specifically PandaX-xT (200 ton-year exposure), will be able to probe the entire allowed parameter space of this window via SI searches.
• Higgs Invisible Decay: In this window, the branching ratio for $h \to \chi\chi$ is enhanced to the order of $10^{-3}$, potentially detectable at future colliders.

C. Collider Signatures at ILC

• Channel Selection: The di-lepton channel ($e^+e^- \to \ell^+\ell^- \chi\chi$) is found to be superior to the mono-photon channel due to Vector Boson Fusion (VBF) enhancement and lower backgrounds.
• Kinematic Cuts: By applying cuts on missing transverse energy ($E_T^{miss} > 100$ GeV), di-lepton invariant mass ($700 < M_{\ell\ell} < 850$ GeV), and leading lepton transverse momentum ($P_T^{\ell_1} < 140$ GeV), backgrounds are significantly suppressed.
• Discovery Potential:
  • For the surviving mass range, only a very narrow sub-window $58.7 \text{ GeV} \lesssim m_\chi \lesssim 59.3 \text{ GeV}$ can be probed with statistical significance $> 2\sigma$ at the ILC ($\sqrt{s}=1$ TeV, $4 \text{ ab}^{-1}$).
  • Using polarized beams ($P_{e^+} = +20\%, P_{e^-} = -60\%$) improves the significance to $\sim 2.5\sigma$.

4. Significance

• Unified Solution: The paper validates the scotogenic inverse seesaw model as a viable framework that simultaneously explains neutrino masses and Dark Matter without fine-tuning Yukawa couplings to unreasonably small values (unlike scalar DM scenarios).
• Experimental Guidance: It provides a clear target for future experiments:
  • Direct Detection: PandaX-xT and XENONnT are crucial for testing the Higgs resonance window.
  • Colliders: The ILC offers a complementary probe, specifically sensitive to the lower edge of the viable mass window ($58.7-59.3$ GeV) via di-lepton signatures.
• Phenomenological Insight: The study highlights the critical role of the Majorana nature of DM in suppressing SI interactions, shifting the primary constraint from SI to SD limits, which effectively carves out the Z-resonance region and isolates the Higgs resonance as the only surviving light DM candidate in this model.

In conclusion, the paper establishes a robust, testable "light fermionic DM window" ($58-63$ GeV) that is consistent with all current neutrino, flavor, and cosmological data, and predicts specific signatures for upcoming direct detection and collider experiments.