⚛️ phenomenology

Dark photon portal dark matter with low-temperature reheating

This paper demonstrates that a low-temperature reheating scenario, which dilutes dark matter relic density through delayed inflaton decay, allows dark photon-mediated dark matter to evade current multi-experimental constraints by requiring a significantly smaller kinetic mixing parameter across complex scalar, Dirac, and Majorana fermion models.

Original authors: Zhi-Long Han, Honglei Li, Ang Liu, Lei Wu, Cai-Xia Yang

Published 2026-09-22

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CC BY 4.0

Original authors: Zhi-Long Han, Honglei Li, Ang Liu, Lei Wu, Cai-Xia Yang

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 stars and galaxies in our universe are only a small 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 know it is there, we have no idea what it is made of. One leading idea suggests that dark matter consists of new, heavy particles that rarely bump into ordinary matter. To explain how these particles might have formed in the early universe and why they are still around today, physicists often imagine a hidden force that connects the dark world to our own. This force would be carried by a particle called a dark photon, acting as a bridge that allows dark matter to occasionally speak with the particles we can see.

However, this simple picture has run into a wall. If dark matter formed in the standard way, the strength of the connection between the dark photon and ordinary matter would need to be just right to produce the amount of dark matter we observe today. But when scientists calculated this, they found that the required connection was so strong that it should have been easily spotted by sensitive detectors on Earth or by telescopes looking at the cosmos. Since no one has seen it, the standard version of this theory seems to be ruled out. The universe appears to be hiding its dark matter in a way that makes it much harder to find than the simplest models predicted.

A team of researchers has now proposed a different history for the early universe that could explain this silence. They suggest that the universe did not heat up to the temperatures we usually assume right after the Big Bang. Instead, they imagine a period where the universe remained relatively cool for a longer time because a heavy particle, known as the inflaton, took a long time to decay into the radiation that fills space. This delay meant that the universe reheated at a much lower temperature than previously thought. This change in the cosmic timeline has a profound effect: it dilutes the amount of dark matter left over from the early days. Because there is less dark matter to begin with, the connection between the dark photon and ordinary matter can be much weaker than the standard models require. A weaker connection means the dark matter is far more elusive, allowing it to slip past the strict limits set by current experiments.

The researchers explored this scenario by building a detailed model where dark matter interacts with our world only through this dark photon bridge. They tested three different types of dark matter particles: complex scalar particles, which are like simple points in space; Dirac fermions, which are the kind of matter that makes up electrons and protons; and Majorana fermions, which are their own antiparticles. In each case, they simulated how these particles would have behaved if the universe had reheated at a low temperature, specifically looking at scenarios where the temperature was just a few million degrees, far below the trillions of degrees usually assumed.

Their calculations showed that this low-temperature history opens up a new window of possibility. In the standard, high-temperature scenario, the models they tested were completely ruled out by data from direct detection experiments, which look for dark matter hitting atoms in deep underground tanks, and by collider experiments, which smash particles together to look for missing energy. But with the low-temperature reheating, the required connection between dark matter and ordinary matter becomes so weak that it falls below the current detection limits. This means the dark matter could exist exactly as the theory predicts, but it has simply been too faint to see so far.

The study found that for the complex scalar and Dirac fermion cases, the most promising way to find this hidden matter in the future is through even more sensitive direct detection experiments. These future detectors could potentially see dark matter particles with masses ranging from a tiny fraction of a proton's mass up to about ten times that mass, provided the connection to ordinary matter is extremely weak. For the Majorana fermion case, the situation is different because these particles do not interact with detectors in the same way. Here, the best hope for discovery lies with future particle colliders, which could look for the dark photons being produced in high-energy collisions.

Crucially, the researchers also confirmed that the standard, high-temperature version of this theory is effectively dead. If the universe reheated as traditionally thought, the dark matter would have to interact with us much more strongly, and the fact that we haven't seen it means that specific version of the story is incorrect. The new low-temperature scenario does not just tweak the numbers; it fundamentally changes the conditions under which dark matter formed, allowing it to survive in a state that is consistent with all current observations. While the paper relies on simulations and theoretical calculations rather than new experimental data, it provides a clear roadmap for where to look next. It suggests that the dark matter we are searching for might not be hiding behind a wall of strong interactions, but rather in a quiet, weakly connected corner of physics that only a cooler, slower early universe could have created.

Technical Summary: Dark Photon Portal Dark Matter with Low-Temperature Reheating

Problem Statement
The paper addresses the tension between the dark photon ( $A'$ ) portal model of dark matter (DM) and current experimental constraints. In the conventional non-resonant benchmark scenario, where the dark photon mass is three times the DM mass ( $m_{A'}/m_\chi = 3$ ), the kinetic mixing parameter ( $\epsilon$ ) required to produce the observed relic density is typically ruled out by a combination of direct detection, indirect detection, and collider constraints. While resonant scenarios or specific mass ratios (e.g., $1 \lesssim m_{A'}/m_\chi \lesssim 2$ ) can evade these bounds, the standard non-resonant case remains highly challenged. The authors investigate whether a low-temperature reheating mechanism, driven by the delayed decay of the inflaton, can dilute the DM relic density sufficiently to allow smaller values of $\epsilon$ , thereby enabling the model to survive current multi-experimental bounds.

Methodology
The authors employ a simplified model where a dark photon $A'$ mediates interactions between Standard Model (SM) fermions and a singlet dark matter particle $\chi$ . They consider three distinct DM candidates: complex scalar, Dirac fermion, and Majorana fermion. The interaction Lagrangian includes kinetic mixing $\epsilon$ between the dark photon and the SM hypercharge/photon fields, and a coupling $g_\chi$ between the dark photon and the DM current.

The study incorporates a low-temperature reheating scenario where the inflaton $\phi$ decays into SM radiation with a decay width $\Gamma_\phi$ . This process injects entropy into the universe, lowering the reheating temperature ( $T_{rh}$ ) to scales potentially comparable to or lower than the DM freeze-out temperature ( $T_{fo}$ ). The cosmological evolution is modeled using Boltzmann equations for the inflaton energy density, SM entropy density, and DM number density. The authors solve these equations using micrOMEGAs to calculate the DM relic density, accounting for the dilution effect caused by entropy production.

The viable parameter space is constrained by:

Direct Detection: Nuclear and electron recoil experiments (e.g., XENONnT, PandaX-4T, DarkSide-50).
Indirect Detection: Constraints from CMB anisotropies (Planck) and astrophysical observations (AMS, Fermi-LAT, H.E.S.S.).
Collider Searches: Limits on invisible $A'$ decays from NA64, BABAR, BESIII, and LEP, as well as monophoton searches.
Electroweak Precision Tests (EWPT): Constraints on $\epsilon$ from $Z$ -boson observables.
Big Bang Nucleosynthesis (BBN): The requirement that $T_{rh} \gtrsim 4$ MeV.

Key Contributions and Results
The paper systematically explores the parameter space for the three DM scenarios under the combined experimental constraints, focusing on the benchmark $m_{A'}/m_\chi = 3$ and $\alpha_\chi = 0.5$ .

Complex Scalar DM:
- The conventional WIMP scenario is completely ruled out by direct detection limits.
- With low $T_{rh}$ ( $4 \text{ MeV} \lesssim T_{rh} \lesssim \mathcal{O}(100) \text{ MeV}$ ), the model survives for $m_\chi \lesssim 10$ GeV and $\epsilon \lesssim \mathcal{O}(10^{-4})$ .
- Future direct detection experiments are projected to probe $0.18 \text{ GeV} \lesssim m_\chi \lesssim 10$ GeV with $10^{-8} \lesssim \epsilon \lesssim 10^{-4}$ . This range is significantly broader than what future collider experiments can access.
Dirac Fermion DM:
- Similar to the scalar case, the WIMP benchmark is excluded.
- Due to s-wave annihilation, indirect detection constraints are more stringent than in the scalar case, leading to a shrinkage of the allowed parameter region for $\epsilon \lesssim 2.5 \times 10^{-5}$ relative to the complex scalar case.
- Future direct detection remains the most promising probe, capable of testing $0.2 \text{ GeV} \lesssim m_\chi \lesssim 10$ GeV with $10^{-8} \lesssim \epsilon \lesssim 10^{-5}$ . Future indirect detection and collider sensitivities are largely excluded by current constraints.
Majorana Fermion DM:
- Direct detection constraints are absent due to the axial-vector nature of the interaction (velocity suppression).
- Indirect detection limits are weak due to p-wave suppression.
- Consequently, collider constraints become the dominant limit for light masses ( $m_\chi \lesssim 2.7$ GeV), excluding $\epsilon \gtrsim 10^{-4}$ .
- Future colliders may probe $0.1 \text{ GeV} \lesssim m_\chi \lesssim 1.8$ GeV with $\epsilon \sim \mathcal{O}(10^{-5})$ . EWPT constraints become relevant for larger masses but only probe a small fraction of the parameter space.

Significance and Claims
The paper claims that the low-temperature reheating mechanism offers a viable pathway for dark photon portal dark matter to evade the stringent constraints that currently rule out the conventional non-resonant WIMP benchmark. By diluting the relic density through entropy production, the model allows for significantly smaller kinetic mixing parameters ( $\epsilon$ ), which are consistent with observational data.

The authors conclude that while the standard WIMP scenario with $m_{A'}/m_\chi = 3$ is nearly ruled out across all three DM types, the low- $T_{rh}$ scenario remains viable. The primary discovery potential lies in future direct detection experiments for scalar and Dirac fermion DM, whereas collider searches are the primary avenue for Majorana fermion DM. The study highlights that the accessible parameter space for Majorana DM is far more restricted compared to the scalar and Dirac cases.

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