Probing inelastic sub-GeV dark matter at the DUNE near detector

This paper investigates the sensitivity of the DUNE near detector's liquid argon cube to sub-GeV inelastic dark matter within a UV-complete framework featuring a dark Higgs mechanism, demonstrating its unique ability to probe parameter space consistent with the observed relic abundance, particularly in regions where traditional decay-based searches are ineffective.

The Gist

The Invisible Ghost Hunt: How DUNE Might Catch "Bouncy" Dark Matter

Imagine the universe is a giant, dark ocean. We know there's something massive swimming in it—Dark Matter—because we can see the waves it makes on the surface (the gravity holding galaxies together). But we've never seen the fish itself.

For decades, scientists have been looking for a specific type of fish called a WIMP (Weakly Interacting Massive Particle). It's like looking for a whale in the ocean. But recently, the ocean has been empty of whales. So, scientists are now looking for something much smaller: sub-GeV Dark Matter. Think of these as tiny, invisible minnows.

This paper proposes a new theory about what these minnows look like and how we might catch them using a giant experiment called DUNE (Deep Underground Neutrino Experiment).

Here is the story of their hunt, broken down into simple concepts.

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1. The Theory: The "Bouncy" Dark Matter

Usually, scientists imagine Dark Matter as a single, solid particle. But this paper suggests a different idea: Inelastic Dark Matter (iDM).

The Analogy: The Two-Story House
Imagine Dark Matter isn't just one person, but a pair of twins living in a two-story house.

• The Ground Floor (χ₁): This is the "light" version. It's stable and makes up the Dark Matter we see today.
• The Second Floor (χ₂): This is the "heavy" version. It's unstable and wants to fall down to the ground floor.

In this model, the "stairs" between the floors are a bit tricky. To get from the heavy version to the light version, the particle has to "bounce" or change its state. This is called inelastic scattering. It's like trying to jump from a high diving board into a pool; you need a specific amount of energy to make the jump.

The Secret Elevator (The Dark Higgs)
The paper adds a twist: The reason these two floors exist is because of a "Dark Higgs" field. Think of this as a secret elevator mechanism that splits the twins apart. This mechanism also creates a new force carrier called the Dark Photon, which acts like a messenger between our world and the dark world.

2. The Problem: Why We Haven't Found Them Yet

Scientists have been looking for these particles by watching them decay (fall apart) or by waiting for them to bump into regular matter.

The Analogy: The Silent Alarm
If the "Dark Photon" is heavy compared to the Dark Matter, the "heavy twin" (χ₂) becomes very stable. It's like a ghost that refuses to leave the house.

• Old Search Methods: Most experiments look for the ghost leaving the house (decaying) and leaving a trail of smoke.
• The Issue: If the ghost is too stable (because the "Dark Photon" is heavy), it never leaves the house. It just sits there, invisible. The old search methods fail because they are waiting for a smoke signal that never comes.

This is where the paper gets interesting. It says, "Don't wait for the ghost to leave the house. Let's see if we can make the ghost bounce off the walls."

3. The Solution: The DUNE Near Detector

The authors suggest using DUNE, a massive experiment in the US designed to study neutrinos (ghostly particles from the sun and stars).

The Setup: The Giant Fish Tank
DUNE has a "Near Detector" filled with a giant cube of liquid argon (frozen argon gas). It's like a massive, ultra-clear fish tank sitting right next to the particle accelerator.

• The Beam: Scientists shoot a beam of protons at a target. This creates a shower of particles, including our invisible Dark Matter minnows.
• The Trap: These minnows fly through the tank. Most pass right through without touching anything. But occasionally, one might bump into an electron in the argon.

The "Bounce" Signal
When a Dark Matter particle bumps into an electron, it doesn't just bounce off; it might change its state (the "inelastic" part).

• If it's the light twin (χ₁), it might get hit and turn into the heavy twin (χ₂).
• If it's the heavy twin (χ₂), it might get hit and drop down to the light twin (χ₁).

This "bounce" gives the electron a tiny kick. The liquid argon detector is so sensitive it can see this tiny kick, even though the Dark Matter itself is invisible.

4. Why This is a Big Deal

The paper runs simulations to see if DUNE can actually see this.

• The "Forbidden" Zone: There are parts of the universe where the "heavy twin" is so stable that it never decays. Traditional experiments (like NA64 or BABAR) look for decays, so they are blind to this area. It's like trying to find a silent ghost by listening for a scream.
• DUNE's Superpower: Because DUNE looks for the bounce (scattering) rather than the scream (decay), it can see the silent ghost.
• The Result: The paper shows that DUNE could detect Dark Matter in these "forbidden" zones, especially when the Dark Photon is much heavier than the Dark Matter. It's like finding a new way to see in the dark that no one else has thought of.

5. The Takeaway

This paper is a roadmap for a new kind of treasure hunt.

1. The Treasure: Sub-GeV Dark Matter that exists in a "two-state" system (Inelastic Dark Matter).
2. The Obstacle: The treasure is hiding in a zone where it refuses to decay, making it invisible to current detectors.
3. The New Tool: The DUNE experiment, specifically its liquid argon tank, can act as a giant net that catches the treasure by feeling the "bounce" when it hits an electron.

In short: If Dark Matter is a shy ghost that refuses to leave its room, this paper suggests we stop waiting for it to walk out the door. Instead, we should shake the walls (the liquid argon) and see if we can feel it bumping around inside. DUNE might just be the first to feel that bump.

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains unknown. While Weakly Interacting Massive Particles (WIMPs) have been the primary focus, the lack of signals at the electroweak scale has shifted attention to sub-GeV candidates. A specific class of models, Inelastic Dark Matter (iDM), proposes that the DM particle is a Dirac fermion split into two non-degenerate Majorana states ($\chi_1$ and $\chi_2$) with a small mass splitting $\Delta$.

The Core Challenge:
In standard iDM models where the dark photon mass is generated via the Stueckelberg mechanism, the DM relic abundance is often set by the annihilation channel $\chi_1 \chi_2 \to \text{SM fermions}$. However, this process is an $s$-wave interaction that remains efficient at low velocities, leading to strong constraints from the Cosmic Microwave Background (CMB) regarding energy injection during recombination.

The Specific Gap:
Recent studies suggest that if the dark photon mass arises from a Dark Higgs mechanism (spontaneous breaking of a $U(1)_D$ symmetry by a scalar field $\phi$), new annihilation channels open up. Specifically, the process $\chi_1 \chi_1 \to h' h'$ (where $h'$ is the dark Higgs) becomes relevant. These channels can be "forbidden" (kinematically closed at zero temperature but open via thermal tails) or $p$-wave suppressed, potentially evading CMB constraints. However, these scenarios often push the viable parameter space toward regions with large dark photon-to-DM mass ratios ($R = m_{A'}/m_1$) and small kinetic mixing ($\epsilon$), making them difficult to probe with traditional decay-based searches (which rely on the decay of the heavier state $\chi_2$).

2. Methodology

Theoretical Framework

The authors propose a minimal, ultraviolet-complete model extending the Standard Model (SM) with:

• A $U(1)_D$ gauge symmetry mediated by a dark photon ($A'$).
• A Dirac fermion $\psi$ that splits into two Majorana states ($\chi_1, \chi_2$) upon symmetry breaking.
• A complex scalar field $\phi$ (Dark Higgs) responsible for the symmetry breaking and mass generation.
• Key Parameters: DM mass ($m_1$), mass splitting ($\Delta$), kinetic mixing ($\epsilon$), dark gauge coupling ($\alpha_X$), mass ratio ($R = m_{A'}/m_1$), dark Higgs mass ($m_{h'}$), and mixing angle ($\theta$).

Relic Abundance Calculation

• Tools: The Boltzmann equations were solved numerically using micrOMEGAs, implemented via LanHEP and FeynRules.
• Dynamics: The study analyzes the interplay between the standard inelastic channel ($\chi_1 \chi_2 \to \bar{f}f$) and the new Dark Higgs-mediated channels ($\chi_1 \chi_1 \to h' h'$).
• Stability: The model ensures $\chi_1$ is stable while $\chi_2$ decays (dominantly via $\chi_2 \to \chi_1 \bar{f}f$) with a lifetime short enough to avoid Big Bang Nucleosynthesis (BBN) constraints.

Experimental Simulation (DUNE)

The study focuses on the DUNE Near Detector Liquid Argon (ND-LAr) cube.

• Production: DM is produced via neutral meson decays ($\pi^0, \eta \to \gamma A' \to \gamma \chi \chi$) and proton bremsstrahlung ($pN \to pN A'$) using Pythia 8.3 and MadGraph/MadDump.
• Detection: The primary signal is Dark Matter-Electron scattering ($\chi_{1,2} + e^- \to \chi_{1,2} + e^-$).
  • Mediator: The interaction is dominated by the dark photon ($A'$) due to the suppression of the Dark Higgs channel by the small electron Yukawa coupling.
  • Kinematics: The analysis utilizes the variable $E_e \theta^2$ (electron energy $\times$ scattering angle squared) to distinguish DM signals from the dominant neutrino background (elastic $\nu-e$ scattering and CCQE).
• Scenarios: Two configurations were simulated:
  1. On-axis: Standard neutrino beam operation (7 years, $1.1 \times 10^{21}$ POT/year).
  2. Beam-dump: Protons directed to a dump to suppress neutrino flux by $10^3$, allowing sensitivity with shorter run times (6 months).
• Statistical Analysis: A $\chi^2$ test with pull parameters (flux, detector, and background uncertainties) was used to determine exclusion limits at 90% Confidence Level (CL).

3. Key Contributions

1. UV-Complete iDM Model: The paper moves beyond phenomenological iDM models by explicitly including the Dark Higgs sector. It demonstrates how the Dark Higgs naturally induces the mass splitting and opens new annihilation channels ($\chi_1 \chi_1 \to h' h'$) that are crucial for satisfying relic density constraints without violating CMB bounds.
2. Relevance of "Forbidden" and $p$-wave Channels: The authors show that for specific mass ratios ($m_{h'} \approx m_1$), the annihilation into Dark Higgs pairs dominates or significantly alters the relic abundance, shifting the viable parameter space to regions where the kinetic mixing $\epsilon$ is very small.
3. Complementarity of Scattering vs. Decay Searches: The paper highlights a critical limitation of current fixed-target experiments: they often rely on detecting the decay of the heavier DM state ($\chi_2 \to \chi_1 e^+ e^-$). In regimes with large mass ratios ($R$), $\chi_2$ becomes long-lived and stable on detector scales, rendering decay searches blind. The study proves that scattering searches (DM-electron interactions) remain sensitive in these "blind" regions.
4. DUNE ND-LAr Sensitivity: A comprehensive sensitivity projection for the DUNE experiment, specifically for the sub-GeV iDM scenario with a Dark Higgs, is provided.

4. Results

• Relic Abundance: The inclusion of the Dark Higgs channel significantly enlarges the parameter space compatible with the observed relic density.
  • Blue Region (Pure Inelastic): Dominated by $\chi_1 \chi_2 \to \bar{f}f$.
  • Green Region (Forbidden): Dominated by thermal tail effects allowing $\chi_1 \chi_1 \to h' h'$.
  • Red Region ($p$-wave): Dominated by $\chi_1 \chi_1 \to h' h'$ when kinematically open but $p$-wave suppressed.
• DUNE Sensitivity:
  • Standard On-axis Mode: For the benchmark $R=3$, DUNE has limited sensitivity to the relic-abundance-consistent regions. However, for larger mass ratios ($R=10$), DUNE can probe the region $10 \text{ MeV} \lesssim m_1 \lesssim 15 \text{ MeV}$ with $y \sim 10^{-12}$ (where $y = \alpha_X \epsilon^2 (m_1/m_{A'})^4$).
  • Beam-Dump Mode: This configuration significantly extends the reach, allowing sensitivity up to $m_1 \sim 20 \text{ MeV}$ and probing lower values of $y$ (down to $10^{-13}$).
• Large Mass Ratios ($R$): The study identifies that for large $R$ (e.g., $R > 10$), the heavier state $\chi_2$ is highly stable, making decay-based searches (like NA64 or BABAR) ineffective. DUNE's ability to detect scattering events allows it to probe these large-$R$ regions, which are currently unconstrained.
• Parameter Space Coverage: The results show that DUNE can access thermal iDM scenarios that are otherwise inaccessible, particularly where the Dark Higgs mechanism dictates the relic density.

5. Significance

• Exploring the "Dark Higgs" Portal: This work demonstrates that the Dark Higgs is not just a mass generator but a critical component that reshapes the phenomenology of sub-GeV DM, creating viable parameter spaces that evade standard constraints.
• Overcoming the "Decay Blind Spot": It establishes that fixed-target experiments like DUNE are uniquely positioned to probe iDM scenarios where the heavier DM state is stable. By focusing on scattering rather than decay, DUNE complements existing exclusion limits from experiments like NA64 and BABAR.
• Future of Sub-GeV Searches: The paper validates the potential of the DUNE Near Detector to serve as a powerful dark matter search facility, capable of exploring thermal relic scenarios with extended dark sectors that are difficult to access via direct detection or collider searches.
• Methodological Benchmark: The detailed simulation of DM production, propagation, and detection in a Liquid Argon TPC, including realistic background rejection techniques ($E_e \theta^2$ cuts), provides a robust framework for future analyses of sub-GeV DM at neutrino facilities.

In conclusion, the paper argues that the DUNE ND-LAr is a critical tool for testing UV-complete inelastic dark matter models, specifically those involving a Dark Higgs, by accessing parameter regions (large mass ratios, small mixing) that are currently invisible to decay-based searches.