⚛️ phenomenology

Interacting scalar-fermion two-component dark matter in a gauged $\boldsymbol{U(1)_{B-L}}$ model

This paper proposes a viable two-component dark matter model within a gauged $U(1)_{B-L}$ extension of the Standard Model, where a Dirac fermion and a complex scalar interact via Yukawa coupling to achieve a genuinely coupled freeze-out that satisfies collider and direct detection constraints while remaining testable by future experiments.

Original authors: Jacinto P. Neto, Farinaldo S. Queiroz, Carlos E. Yaguna

Published 2026-11-03

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CC BY 4.0

Original authors: Jacinto P. Neto, Farinaldo S. Queiroz, Carlos E. Yaguna

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

For decades, astronomers have known that the visible universe—stars, planets, and the gas between them—makes up only a tiny fraction of what exists. The rest is an invisible substance called dark matter, which holds galaxies together through its gravity but refuses to interact with light. While we can see its effects, we have never directly detected a single particle of it. The leading theory for years has been that dark matter consists of a single type of heavy particle that occasionally bumps into normal matter or destroys itself in pairs. However, as sensitive detectors have failed to find these particles, physicists have begun to consider a more complex possibility: that the dark sector might be a bustling community of different species, interacting with one another in ways we have not yet imagined.

In this new study, researchers propose a specific model where dark matter is not a single lonely particle, but a pair of distinct entities that constantly transform into one another. They suggest a universe where a heavy fermion (a type of particle similar to the electron) and a complex scalar (a type of particle similar to the Higgs boson) coexist and are locked in a dynamic relationship. Unlike previous models that required invisible rules to keep these particles stable, this team found a way to make them stable using the fundamental forces of nature themselves. By extending the Standard Model of physics with a new force carrier, they created a scenario where these two dark particles can swap identities, annihilate, or convert into each other, all while remaining hidden from our current telescopes.

The researchers built their model around a new force called $U(1)_{B-L}$ , which is a variation of the forces we already know. In this framework, they introduced two new dark particles: a fermion and a scalar. The key innovation is that these two particles are not independent; they are directly linked by a specific interaction that allows them to change into one another. If the scalar particle is heavy enough, it can decay into two fermions, but the team set the rules so that the scalar is lighter than two fermions combined. This kinematic condition ensures that neither particle can decay into the other, making both of them stable and capable of surviving from the early universe until today. This stability is achieved without inventing new, arbitrary symmetries, relying instead on the natural laws of the model.

To understand how this pair of particles would behave over the history of the universe, the team ran detailed computer simulations of the early cosmos. They tracked how the abundance of these particles changed as the universe cooled down. In the standard view, dark matter particles simply freeze out and stop interacting. Here, the process is much more active. The two particles engage in a constant exchange: two fermions can turn into a scalar and a burst of energy, or a scalar can turn into two fermions. These "semi-conversion" and "semi-annihilation" processes couple the fate of the two species. The simulations showed that this coupled behavior allows the model to produce exactly the amount of dark matter we observe in the universe today, even when the particles are not sitting at a specific mass that would make them annihilate more easily.

The study examined two main scenarios: one where the fermion is lighter than the scalar, and another where the scalar is lighter. In both cases, the researchers found that the final mix of dark matter is not determined simply by which particle is lighter. Instead, the balance depends on the strength of the interactions between them. In some regions of their model, the fermion dominates the dark matter density; in others, the scalar takes the lead. Crucially, they found that the correct amount of dark matter can be achieved without relying on a "resonance," a specific mass condition that often makes models too fragile to be realistic. The particles can reach the right abundance through their complex interactions even when they are far from these special mass points.

The team then tested their model against real-world data to see if it could survive the scrutiny of modern experiments. They checked the model against constraints from particle colliders, which search for the new force carrier particle, and against direct detection experiments that look for dark matter hitting atomic nuclei. The results were encouraging. While the model is tightly constrained by current limits—particularly because the new force carrier must be heavy enough to have escaped detection so far—there remains a significant portion of the parameter space that is still viable. This means there are still many combinations of particle masses and interaction strengths that fit all known data. Furthermore, the researchers noted that the next generation of ultra-sensitive detectors, which are currently being planned, will be able to probe a large part of this remaining space.

One of the most robust findings of the paper is that the specific details of the particles' charges do not drastically change the outcome. The team tested their model with different values for the dark matter particles' charges and found that the overall behavior of the system remained consistent. Whether the charge was slightly higher or lower, the model still produced viable solutions where the two components of dark matter coexist and interact. This suggests that the core idea of a coupled two-component dark sector is a stable and flexible concept, not a fluke of a single specific choice of numbers.

Ultimately, this work offers a fresh perspective on the dark matter puzzle. It moves away from the idea of a single, static particle and embraces a more dynamic, interacting dark sector. By showing that two different types of particles can stabilize each other and jointly account for the missing mass of the universe, the study opens up new avenues for exploration. It suggests that the answer to the dark matter mystery might not be a single discovery, but a complex interplay of particles that we are only just beginning to understand. The path forward is clear: as new experiments come online, they will be able to test these specific predictions, potentially revealing the first signs of this hidden, interacting dark world.

Technical Summary: Interacting Scalar–Fermion Two-Component Dark Matter in a Gauged U(1) $_{B-L}$ Model

Problem and Motivation
The particle nature of dark matter (DM) remains unknown. While the Weakly Interacting Massive Particle (WIMP) paradigm traditionally assumes a single DM species generated via thermal freeze-out, the absence of non-gravitational signals has constrained simple single-component realizations. An alternative is a multi-component dark sector where the observed density is shared among multiple stable particles. A central challenge in such models is explaining the stability of multiple DM candidates without invoking ad-hoc discrete symmetries (e.g., $Z_N$ ). This paper proposes a framework where the stability of two distinct DM particles arises naturally from an underlying gauged $U(1)_{B-L}$ symmetry, which simultaneously addresses the origin of neutrino masses via the type-I seesaw mechanism.

Model Framework
The authors extend the Standard Model (SM) with a gauged $U(1)_{B-L}$ symmetry. The minimal anomaly-free implementation includes three right-handed neutrinos ( $N_{iR}$ ) and a complex scalar singlet $\Phi_{BL}$ (charge 2) responsible for symmetry breaking. The dark sector is augmented by two new fields:

A Dirac fermion $\chi$ (charge $n_\chi$ ).
A complex scalar $S$ (charge $-2n_\chi$ ).

The charge assignment $Q_{B-L}(S) = -2Q_{B-L}(\chi)$ is crucial. It allows for a gauge-invariant, renormalizable Yukawa interaction:
$\mathcal{L} \supset \frac{1}{2} S \chi^c (y_s + y_p \gamma_5) \chi + \text{H.c.}$
This interaction directly couples the two DM components. Stability is ensured kinematically and by gauge invariance:

Fermion $\chi$ : Stable because no renormalizable operator allows its decay into lighter states.
Scalar $S$ : Stable provided the kinematic condition $m_S < 2m_\chi$ is met, preventing the decay $S \to \chi\chi$ .
No additional discrete symmetry is required; stability is a consequence of the gauge structure and mass hierarchy.

Methodology
The authors perform a comprehensive numerical analysis of the model's parameter space using the following steps:

Theoretical Consistency: Imposing vacuum stability (boundedness from below) and ensuring the vacuum configuration $\langle S \rangle = 0$ is a local minimum.
Experimental Constraints: Applying limits from:
- Colliders: Higgs signal strengths (ATLAS/CMS), heavy scalar searches ( $h_2$ ), and $Z'$ searches in dilepton channels (restricting $m_{Z'} \geq 4$ TeV).
- Direct Detection: Spin-independent (SI) scattering limits from XENONnT and LZ, accounting for the fact that each component constitutes only a fraction ( $\xi_X$ ) of the total local DM density.
- Indirect Detection: Approximate constraints from Fermi-LAT and H.E.S.S. on annihilation and semi-conversion rates.
Relic Abundance Calculation: Solving a system of coupled Boltzmann equations for the comoving abundances $Y_\chi$ $Y_{χ}$ and $Y_S$ $Y_{S}$ . The system includes:
- Standard annihilation ($1100, 2200$).
- Conversion ($1122, 2211$).
- Semi-conversion ($1120 $:$ \chi\chi \to S^\dagger X^0$).
- Semi-annihilation ($1210 $:$ \chi S \to \bar{\chi} X^0$).
  The total relic density is $\Omega_{DM}h^2 = \Omega_\chi h^2 + \Omega_S h^2$ , constrained to $0.120 \pm 0.001$ .
Parameter Scan: A global scan using a differential-evolution algorithm over masses ( $m_\chi, m_S, m_{Z'}, m_{h_2}$ ), couplings ( $g_{BL}, y_s, y_p, \lambda_{SH}, \lambda_{S\Phi}$ ), and mixing angles. The benchmark charge is $n_\chi = 3/4$ , with checks performed for $n_\chi = 2/5$ and $7/5$ .

Key Results
The analysis identifies viable solutions for both mass hierarchies: $m_S > m_\chi$ and $m_S < m_\chi$ .

Coupled Freeze-Out Dynamics: The relic abundances are not determined by independent freeze-outs but by a coupled network.
- In the $m_S > m_\chi$ regime, the fermion $\chi$ typically dominates the relic density. The semi-conversion process ( $\chi\chi \to S^\dagger X^0$ ) is the primary depletion mechanism for $\chi$ , while simultaneously acting as a source for $S$ .
- In the $m_S < m_\chi$ regime, the relic composition is more varied (scalar-dominated, fermion-dominated, or mixed). The final composition results from a competition between scalar depletion (annihilation) and fermion-to-scalar transfer (conversion/semi-conversion).
Non-Resonant Viability: Contrary to many simplified models, viable solutions exist over broad regions away from the $Z'$ resonance ( $m_{Z'} \approx 2m_{DM}$ ). The correct relic abundance is achieved through the interplay of the gauge portal ( $Z'$ ), scalar portal ( $h_{1,2}$ ), and dark Yukawa interactions, rather than relying on resonant enhancement.
Direct Detection: Direct detection provides the strongest constraint, particularly on the fermion component via $Z'$ exchange and on the scalar via $Z'$ and Higgs exchange. Despite these tight bounds, a significant portion of the parameter space survives and remains within the projected sensitivity of next-generation experiments like DARWIN/XLZD.
Charge Independence: The phenomenological features (relic composition, viable parameter space structure) are largely robust against variations in the dark $B-L$ charge $n_\chi$ (tested for $2/5, 3/4, 7/5$ ). While the $Z'$ -mediated annihilation rate scales as $n_\chi^2$ , the total relic abundance and detection prospects remain qualitatively unchanged due to the compensating effects of scalar and Yukawa interactions.

Significance and Claims
The paper claims to demonstrate that a genuinely interacting two-component dark matter model can be realized within a well-motivated $U(1)_{B-L}$ extension of the SM without ad-hoc discrete symmetries. The key significance lies in:

Natural Stability: Showing that multiple DM candidates can be stabilized solely by gauge symmetry and kinematic constraints.
Dynamics: Establishing that semi-conversion and conversion processes can qualitatively alter freeze-out dynamics, decoupling the relic abundance from the direct detection cross-sections in ways not possible in single-component models.
Viability: Identifying that the model remains viable even when the $Z'$ resonance is not utilized, suggesting that the observed DM abundance can be reproduced through a complex interplay of dark sector interactions.
Testability: Highlighting that while current direct detection limits are stringent, the model predicts signals within reach of future multi-ton experiments, offering a concrete target for upcoming searches.

The authors conclude that the benchmark choice of $n_\chi = 3/4$ is representative of the broader phenomenology of the model across the explored range of charges.

Technical Summary: Interacting Scalar–Fermion Two-Component Dark Matter in a Gauged U(1)B−L_{B-L}B−L​ Model

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Technical Summary: Interacting Scalar–Fermion Two-Component Dark Matter in a Gauged U(1) $_{B-L}$ Model