Boosted dark matter via semi-annihilation in a radiative neutrino mass model

The Gist

Imagine the universe is filled with a mysterious, invisible substance called Dark Matter. For decades, scientists have been trying to catch a glimpse of it, mostly by waiting for these invisible particles to bump into regular matter (like atoms in a detector) and slow down. But so far, the detectors have come up empty-handed.

This paper proposes a new way to catch Dark Matter. Instead of waiting for slow, lazy particles, the authors suggest looking for Dark Matter that has been "boosted" or supercharged, moving at incredibly high speeds.

Here is the story of how they came up with this idea, explained simply:

1. The "Dark Matter Dance" (Semi-Annihilation)

In the standard story of the universe, Dark Matter particles usually pair up and destroy each other completely (annihilation), turning into pure energy.

But in this paper's model, the Dark Matter particles do something different. They engage in a "semi-annihilation." Imagine two Dark Matter particles meeting. Instead of both disappearing, one of them gets "kicked" out of the dance, while the other transforms into a neutrino (a ghost-like particle that rarely interacts with anything).

The particle that gets kicked out doesn't just wander off slowly; it gets a massive energy boost from the collision. It becomes a Boosted Dark Matter particle, zooming through the galaxy at near-light speed.

2. The "Two-Loop" Recipe (Neutrino Mass)

Why do they think this happens? The authors built a specific "recipe" (a mathematical model) to explain two mysteries at once:

1. Why Dark Matter exists.
2. Why Neutrinos have such tiny masses.

In their recipe, the universe has a hidden symmetry (like a secret rulebook) that keeps things balanced. To make the neutrinos light, they need a complex, two-step cooking process (called a "two-loop" diagram in physics). This same recipe naturally creates the "kick" that turns a slow Dark Matter particle into a fast, boosted one. It's like a single machine that bakes a cake and also launches a rocket; the two processes are linked.

3. The "Speed Trap" (How We Detect It)

So, how do we catch these speeding bullets?

• The Old Way: Traditional detectors are like fishing nets waiting for slow fish. If a Dark Matter particle is moving too fast, it might just zip right through the net without touching anything.
• The New Way: The authors suggest that because these boosted particles are moving so fast, they can smash into protons (the building blocks of atoms) with enough force to be seen.

To make this smash detectable, the model requires a "messenger" particle (a mediator) that is very light—about the weight of a few millionths of a gram (MeV scale). Think of this mediator as a super-light spring. Because it's so light, it can transfer a huge amount of energy when the fast Dark Matter hits it, making the collision loud enough for our detectors to hear.

4. The Future Hunt (DARWIN and DUNE)

The paper calculates that if this model is correct, the next generation of giant detectors will be able to see it.

• DARWIN: A massive tank of liquid xenon (like a giant underwater camera) designed to catch dark matter.
• DUNE: A huge detector filled with liquid argon, usually looking for neutrinos, but also capable of catching these fast Dark Matter particles.

The authors show that if the "messenger" particle is light enough, the chance of a collision (the cross-section) becomes large enough to be seen by these future machines.

Summary

The paper argues that if Dark Matter is part of a more complex family than we thought, it might be "dancing" in a way that creates high-speed runners. These runners are invisible to our current slow-motion detectors, but they will leave a clear trail when they crash into atoms in the massive, next-generation detectors we are building.

The Bottom Line: We might not find Dark Matter by waiting for it to stop; we might find it by catching it while it's running at full speed, thanks to a specific cosmic dance move that also explains why neutrinos are so light.

Technical Summary

Technical Summary: Boosted Dark Matter via Semi-Annihilation in a Radiative Neutrino Mass Model

Problem Statement
The standard thermal freeze-out scenario for dark matter (DM), typically involving $2 \to 2$ annihilation, predicts DM masses in the range of $\mathcal{O}(1)$ MeV to $\mathcal{O}(100)$ TeV. However, null results from direct detection, indirect detection, and collider searches have imposed stringent constraints on these minimal scenarios. While non-minimal extensions (e.g., semi-annihilations, SIMP processes, or multi-component DM) offer alternative pathways, they often lack concrete model realizations that simultaneously address the origin of neutrino masses. Furthermore, standard direct detection experiments lose sensitivity for sub-GeV DM, necessitating alternative signatures. This paper addresses the need for a concrete model where non-standard annihilation processes produce "boosted" dark matter (BDM)—DM particles with kinematically fixed, relativistic energies—while simultaneously generating small neutrino masses radiatively.

Methodology
The authors construct an explicit extension of a two-loop neutrino mass model [10] by introducing a global $U(1)_L$ symmetry (identified as lepton number). The particle content includes:

• Fermions: Standard Model leptons, three generations of singlet Dirac fermions $\psi_i$, and a new Dirac fermion $\chi$.
• Scalars: The SM Higgs doublet $H$, a new doublet $\eta$, a singlet $\chi$, and a singlet $\Sigma$.
• Symmetry Breaking: The singlet scalar $\Sigma$ acquires a vacuum expectation value (VEV), breaking $U(1)_L$ down to a remnant $Z_3$ symmetry.

The model is analyzed through the following steps:

1. Lagrangian and Potential: The BSM Lagrangian includes Yukawa couplings ($y_\nu, y_L, y_\Sigma$) and a scalar potential with 17 real parameters. The scalar sector is diagonalized to determine mass eigenstates ($h, s, \phi, \tilde{\phi}$) and mixing angles ($\theta, \alpha$).
2. Neutrino Mass Generation: Active neutrino masses are generated via two-loop diagrams involving the new scalars and fermions. The authors derive the analytical formula for the neutrino mass matrix $(m_\nu)_{\alpha\beta}$ and establish a correlation between the neutrino Yukawa coupling $y_L$ and the effective neutrino mass $(m_\nu)_{ee}$ relevant for neutrinoless double beta decay.
3. Constraints: The parameter space is constrained by:
   • Charged lepton flavor violation (cLFV), specifically $\mu \to e\gamma$.
   • Electroweak precision tests ($\rho$ parameter and $Z$ boson invisible decay).
   • Higgs mixing angle limits from $K^+ \to \pi^+ + \text{inv}$ and Big Bang Nucleosynthesis (BBN).
   • Vacuum stability conditions on the quartic couplings.
4. Phenomenology: The lightest Dirac fermion $\psi_1$ is identified as the DM candidate. The authors calculate the thermal relic abundance determined by semi-annihilation ($\psi\psi \to \psi\nu$) and standard annihilation ($\psi\psi \to ss$). They then compute the flux of boosted DM produced in the Galaxy and its scattering cross-section with protons mediated by the light scalar $s$.

Key Contributions and Results

• Model Construction: The paper presents a unified framework where the remnant $Z_3$ symmetry, required for the stability of the DM candidate, naturally permits semi-annihilation processes ($\psi\psi \to \psi\nu$) that are forbidden in minimal $Z_2$ symmetric models.
• Neutrino-DM Correlation: A significant finding is the correlation between the neutrino mass sector and DM phenomenology. The Yukawa coupling $y_L$, which governs the semi-annihilation rate, is constrained by the requirement to reproduce observed neutrino masses. The authors show that for the inverted neutrino mass ordering, a relatively large $y_L$ is permitted, which enhances the semi-annihilation cross-section.
• Boosted Dark Matter Signatures:
  • Relic Abundance: Numerical calculations using micrOMEGAs and CalcHEP show that for sub-GeV DM masses, the semi-annihilation channel dominates the determination of the relic abundance ($\Omega_{DM}h^2 = 0.12$).
  • Scattering Cross-Section: The scattering of boosted DM with protons is mediated by the light scalar $s$ (mass $\sim \mathcal{O}(1)$ MeV). The spin-independent cross-section is enhanced to $\mathcal{O}(10^{-36})$ cm$^2$ due to the light mediator mass.
  • Detectability: The authors identify parameter regions where the BDM signal falls within the future sensitivity of the DARWIN (direct detection) and DUNE (neutrino) experiments. Specifically, for a mediator mass $m_s \sim 2$ MeV and specific mass ratios of the $Z_3$-charged scalars ($m_\phi/m_\psi \approx 1.9 - 3.0$), the model predicts detectable events.
• Constraints Satisfaction: The model successfully evades current bounds from cLFV (by assuming diagonal $y_\nu$), electroweak precision tests, and Higgs mixing constraints by choosing appropriate mixing angles ($\sin\theta \sim 10^{-4}$) and heavy scalar masses ($m_\eta, m_{\tilde{\phi}} \sim \text{TeV}$).

Significance
The paper claims that this work provides a concrete realization of boosted dark matter originating specifically from semi-annihilation within a radiative neutrino mass framework. Unlike previous model-independent studies, this work demonstrates how the requirements of neutrino mass generation (specifically the inverted ordering scenario) can naturally lead to the large couplings necessary for observable BDM signals. The authors conclude that if the mediator mass is light ($\mathcal{O}(1)$ MeV), the enhanced scattering cross-section allows future experiments like DARWIN and DUNE to probe this non-minimal dark sector, offering a distinctive signature that distinguishes it from standard thermal DM scenarios. The model also notes that while monochromatic neutrino signals from the Galactic center are marginal, specific resonant tuning could allow for simultaneous detection of both BDM and neutrinos.