GeV-scale thermal dark matter from dark photons: tightly constrained, yet allowed

This paper demonstrates that GeV-scale thermal dark matter in a dark Abelian Higgs model with a Dirac fermion is tightly constrained by direct detection and collider searches, leaving only narrow resonant regions near $m_\chi \approx m_{Z_D}/2$ with small dark sector couplings as viable parameter space where the dark matter can constitute the full observed relic abundance.

The Gist

The Big Picture: The "Invisible Ghost" and the "Messenger"

Imagine the universe is a giant, crowded party. We (the Standard Model particles) are the guests we can see and talk to. Dark Matter is the ghostly guest in the corner that we can't see, but we know is there because the furniture keeps moving when it walks by.

For a long time, scientists have been trying to figure out what this ghost looks like. This paper focuses on a specific type of ghost: a GeV-scale Dark Matter particle (let's call him "Charlie"). Charlie is roughly the weight of a proton or a neutron, but he's invisible.

To interact with us, Charlie needs a messenger. In this story, the messenger is a Dark Photon (let's call her "Diana"). Diana is like a secret agent who can talk to both the invisible ghost (Charlie) and the visible guests (us), but she mostly keeps to herself.

The Problem: The "Too Loud" Ghost

For years, scientists have been setting up traps to catch Charlie.

1. Direct Detection (The Net): Huge tanks of liquid xenon or argon are buried underground. The idea is that if Charlie bumps into a nucleus in the tank, it will make a tiny splash (a recoil).
2. Indirect Detection (The Smoke): If two Charlies bump into each other in space, they might annihilate and create a burst of gamma rays (like a firework). We look for these fireworks in dwarf galaxies.
3. Colliders (The Crash Test): We smash protons together at the LHC to see if we can create Charlie or Diana.

The Bad News: Most of the time, these traps have come up empty. If Charlie were a "loud" ghost (interacting strongly with us), we would have caught him by now. The paper says that for most scenarios, Charlie is ruled out.

The Twist: The "Under-Abundant" Ghost

Here is where the paper gets clever. The authors ask: What if Charlie isn't the only ghost at the party?

Imagine the total amount of dark matter in the universe is a giant pie.

• Scenario A: Charlie makes up the whole pie. If we don't see him, he doesn't exist.
• Scenario B: Charlie is just a small slice of the pie. The rest of the pie is made of some other, even more invisible ghost that we can't detect.

This changes the rules of the game:

• Direct Detection: If Charlie is only a small slice of the pie, he is much rarer in our local neighborhood. He is less likely to bump into our xenon tanks. The "splash" is smaller.
• Indirect Detection: If Charlie is rare, two Charlies bumping into each other is a double rarity. The chance of them meeting and exploding is proportional to the square of his rarity. The "fireworks" become almost non-existent.

The Analogy: Imagine looking for a specific person in a stadium.

• If the stadium is full of only that person, you will definitely see them.
• If the stadium is full of 10,000 people and that person is just one of them, you might miss them.
• If you are looking for two of them to bump into each other, the odds are so low you will almost certainly never see it.

The Solution: The "Resonance" Sweet Spot

The paper finds a very narrow "safe zone" where Charlie can still exist without being caught. It's called the Resonance.

Think of a swing set.

• If you push a swing at the wrong time, it barely moves.
• If you push it at the perfect rhythm (the resonance), it goes huge.

In the early universe, when the temperature was just right, Charlie was produced most efficiently when his mass was exactly half the mass of the Dark Photon messenger ($m_\chi \approx m_{Z_D}/2$).

In this "sweet spot," Charlie was created in huge numbers back then, but because he is so rare now (diluted by the other dark matter), he is too quiet for our current detectors to hear.

The Constraints: How Small Must the Secret Be?

Even in this safe zone, Charlie has to be very shy.

• The Coupling ($\alpha_D$): This is how much Charlie likes to talk to his own kind. The paper says this number must be very small (like $10^{-3}$ or even $10^{-5}$). If he talks too much, he creates too many fireworks (indirect detection) or bumps into us too often (direct detection).
• The Kinetic Mixing ($\epsilon$): This is how much Diana (the messenger) talks to us. If she talks too much, we see her in our particle colliders. If she talks too little, we can't explain how Charlie was made in the first place.

The Future: Closing the Door

The paper concludes that while Charlie can exist, he is hiding in a very tiny closet.

1. Direct Detection: Future experiments (like DARWIN) will be so sensitive they will see even the faintest whispers. They will likely close the door on this scenario unless the "shyness" is extreme.
2. Colliders: Future collider runs will look for the messenger (Diana) more closely. If she exists, they will find her.

Summary in One Sentence

While the universe seems to have ruled out a "loud" dark matter particle, this paper shows that a very shy, rare dark matter particle can still hide in a specific "sweet spot" of mass and interaction strength, waiting for our next-generation, ultra-sensitive detectors to finally catch a glimpse of it.

Technical Summary

1. Problem Statement

GeV-scale thermal Dark Matter (DM) candidates are typically under severe pressure from null results in direct detection (DD), indirect detection (ID), and collider experiments. In simplified models, these constraints often exclude thermal relics up to masses of several tens of GeV.

A critical gap in the literature exists for invisibly decaying dark photons with masses in the range $10 \text{ GeV} \lesssim m_{Z_D} \lesssim m_Z$. This region is above the sensitivity of B-factories (like BaBar) but below the typical sensitivity of LHC searches and electroweak precision observables (EWPO). Furthermore, previous studies often fail to consistently account for scenarios where the DM candidate $\chi$ constitutes only a subdominant component of the total cosmic DM density ($\Omega_\chi < \Omega_{\text{CDM}}$). In such cases, the local DM density and annihilation rates are diluted, affecting DD and ID constraints differently.

Objective: To map the viable parameter space for a Dirac fermionic DM candidate ($\chi$) coupled to a GeV-scale dark photon ($Z_D$) within a Dark Abelian Higgs Model (DAHM), consistently applying constraints from colliders, DD, and ID while accounting for DM density dilution.

2. Theoretical Framework: DAHM-DM

The authors propose a minimally consistent extension of the Standard Model (SM) known as the Dark Abelian Higgs Model with a fermionic DM candidate (DAHM-DM).

• Particle Content:
  • A Dirac fermion $\chi$ (DM candidate) charged under a new dark $U(1)_X$ symmetry.
  • A dark gauge boson $Z_D$ (dark photon).
  • A complex scalar singlet $S$ (dark Higgs) responsible for spontaneously breaking $U(1)_X$ and generating the $Z_D$ mass.
  • Kinetic mixing ($\epsilon$) between the dark $U(1)_X$ and the SM hypercharge $U(1)_Y$.
• Mass Generation:
  • The $Z_D$ acquires mass via the dark Higgs mechanism ($m_{Z_D} \propto g_D w$, where $w$ is the dark Higgs VEV).
  • Mixing occurs between the SM $Z$ boson and $Z_D$, parameterized by a mixing angle $\alpha$.
  • The scalar sector mixes the SM Higgs ($h_{125}$) and the dark Higgs ($h_D$), constrained by Higgs signal strength measurements.
• Thermal Relic Production:
  • The model assumes a standard thermal freeze-out scenario.
  • The dominant annihilation channel is $\chi\bar{\chi} \to f\bar{f}$ (where $f$ is a SM fermion) via $s$-channel $Z_D$ exchange.
  • The analysis focuses on the regime $m_\chi \lesssim m_{Z_D}/2$, where the dark photon decays invisibly into $\chi\bar{\chi}$.
  • Resonance: A key feature is the resonant enhancement of the annihilation cross-section when $m_\chi \approx m_{Z_D}/2$, allowing for the correct relic abundance even with small couplings.

3. Methodology and Constraints

The authors perform a comprehensive scan of the parameter space ($\epsilon, m_\chi, m_{Z_D}, \alpha_D$) by combining three classes of constraints. A crucial methodological step is the consistent application of the dilution factor $\xi = \Omega_\chi / \Omega_{\text{CDM}}$.

A. Direct Detection (DD)

• Mechanism: Spin-independent elastic scattering of $\chi$ off nuclei via $Z$ and $Z_D$ exchange.
• Dilution Effect: The scattering rate is proportional to the local DM density ($\rho_\chi = \xi \rho_0$). Thus, the observable rate scales linearly with $\xi$.
• Key Finding: The theoretical prediction for the effective cross-section $\xi \sigma_{SI}$ is independent of the kinetic mixing $\epsilon$ (since $\sigma_{SI} \propto \epsilon^2$ and $\xi \propto 1/\langle \sigma v \rangle \propto 1/\epsilon^2$).
• Result: DD experiments (XENON1T, LZ, PandaX-4T, DarkSide-50) provide the leading constraints for most of the parameter space. They rule out regions except for narrow bands near the resonance ($m_\chi \approx m_{Z_D}/2$).

B. Indirect Detection (ID)

• Mechanisms:
  1. Gamma Rays: Annihilation in dwarf spheroidal galaxies (Fermi-LAT).
  2. CMB: Energy injection during recombination (Planck).
• Dilution Effect: Annihilation signals scale with the square of the DM density ($\rho_\chi^2 \propto \xi^2$).
• Key Finding: ID constraints are highly sensitive to $\xi$. For subdominant DM ($\xi \ll 1$), the $\xi^2$ suppression significantly relaxes these bounds.
• Result: ID constraints are only stringent when $\xi \approx 1$ (DM constitutes all relic density) and away from the resonance. They fail to probe regions with large kinetic mixing (small $\xi$).

C. Collider Searches

• Mono-X Searches:
  • LHC (Mono-jet): $pp \to \chi\bar{\chi} + j$. Constraints are weak for $m_{Z_D} \sim 10-80$ GeV due to low cross-sections.
  • LEP/BaBar (Mono-photon): $e^+e^- \to \gamma + \chi\bar{\chi}$. Strong constraints for $m_{Z_D} \lesssim 8$ GeV.
• Electroweak Precision Observables (EWPO):
  • Mixing between $Z$ and $Z_D$ modifies $S$ and $T$ parameters.
  • Result: EWPO provides the strongest current limits for invisible dark photons in the $10 \text{ GeV} \lesssim m_{Z_D} \lesssim m_Z$ range.
• Di-lepton Searches:
  • If the dark sector coupling $\alpha_D$ is small, the branching ratio to SM particles ($Z_D \to \ell\ell$) remains significant.
  • Result: Di-lepton limits (BaBar, LHCb, CMS) can surpass mono-X limits for small $\alpha_D$ ($\lesssim 10^{-2}$), even with invisible decays.

4. Key Results

The combination of all constraints reveals a specific "island" of viability:

1. Exclusion of Large Couplings: Scenarios with large dark sector couplings ($\alpha_D \gtrsim 10^{-2}$) are ruled out by DD experiments, even near the resonance.
2. The Viable Window: The only surviving parameter space is in narrow windows close to the resonance ($m_\chi \approx m_{Z_D}/2$).
   • In these regions, $\chi$ can constitute all of the DM ($\xi=1$) or be a subdominant component ($\xi < 1$).
   • Coupling Requirements: To avoid DD limits in these windows, the dark gauge coupling must be small:
     • $\alpha_D \lesssim 10^{-3}$ for $m_\chi < 6$ GeV.
     • $\alpha_D \lesssim 10^{-5}$ for $m_\chi > 10$ GeV.
3. Complementarity of Probes:
   • DD constrains the mass range (excluding non-resonant regions) but is insensitive to $\epsilon$ (due to the $\xi$ scaling).
   • ID constrains the $\xi \approx 1$ region but is blind to subdominant DM with large $\epsilon$.
   • Colliders (EWPO/Di-lepton) constrain the large $\epsilon$ (small $\xi$) region where DD is ineffective.
4. Future Projections:
   • Next-generation DD experiments (DarkSide-LowMass, DARWIN) will probe the allowed resonant regions, pushing the allowed $\alpha_D$ down to $\sim 10^{-4}$.
   • Below this coupling, signals will be hidden by the neutrino fog.
   • Future collider searches will further constrain the kinetic mixing $\epsilon$ for subdominant DM scenarios.

5. Significance and Conclusion

This work demonstrates that GeV-scale thermal dark matter is not entirely excluded, provided the model includes a dark photon mediator and the dark sector coupling is sufficiently small.

• Theoretical Insight: The consistent treatment of the dilution factor $\xi$ is critical. Ignoring it would lead to the incorrect conclusion that the entire GeV-scale parameter space is excluded. The $\xi^2$ suppression of indirect signals allows for large kinetic mixing values that would otherwise be ruled out.
• Phenomenological Impact: The paper identifies a specific, testable region of parameter space (resonant annihilation with small $\alpha_D$) that survives current constraints.
• Experimental Outlook: The remaining viable parameter space is tightly constrained but accessible. It requires a complementary approach:
  • Direct Detection to probe the resonant mass region and lower $\alpha_D$.
  • Collider Searches (specifically EWPO and di-lepton channels) to probe the kinetic mixing $\epsilon$ for subdominant DM scenarios.

In summary, while standard benchmarks are excluded, the DAHM-DM model remains a viable candidate for GeV-scale thermal dark matter, surviving in narrow resonant windows that future experiments are poised to explore.