Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism

This paper proposes a gauged $U(1)_{B-L}$ benchmark model featuring a compressed dark fermion spectrum and a small mixing angle to suppress direct detection constraints, demonstrating that a novel conversion mechanism effectively generates the observed dark matter relic density while remaining consistent with current collider and cosmological limits.

The Gist

The Big Picture: The "Ghost" and the "Heavy Twin"

Imagine the universe is filled with invisible "ghosts" called Dark Matter. Scientists have been trying to figure out how these ghosts interact with the normal stuff we can see (like stars, planets, and us).

Usually, scientists think these ghosts hang out alone and only interact with normal matter through a very weak, invisible handshake. But this paper proposes a new, more interesting story. It suggests that Dark Matter isn't just a lonely ghost; it has a heavier twin brother that is slightly more visible.

The Setup: A New "Messenger" and a "Secret Door"

The paper introduces a new theoretical particle called a $Z'$ boson. Think of this $Z'$ as a messenger or a courier that carries messages between the Dark Matter world and our normal world.

In this story, there are two dark particles:

1. $\chi_1$ (The Dark Matter): The light, stable one that makes up the universe's missing mass. It's like a shy person who wears a heavy disguise (a "mixing angle") so it can't be easily seen.
2. $\chi_2$ (The Heavy Partner): A slightly heavier twin. This one is more "social" and interacts strongly with the messenger ($Z'$).

Because they are twins, they can switch places. The heavy twin ($\chi_2$) can turn into the light one ($\chi_1$), and vice versa, but only if they bump into something else. This "switching" is the Conversion Mechanism.

The Problem: The "Too Loud" Handshake

In older theories, for Dark Matter to exist in the right amount today, it had to shake hands with normal matter quite often. But if it shook hands too loudly, our giant particle detectors (like the ones at the Large Hadron Collider) would have already seen it. They haven't.

This paper says: "What if the Dark Matter is actually very quiet?"
Because the Dark Matter ($\chi_1$) is wearing a disguise (the small mixing angle), it barely talks to normal matter. This explains why we haven't found it yet. But if it's so quiet, how did it survive from the beginning of the universe?

The Solution: The "Crowd Surfing" and "Switching" Strategy

The paper argues that the Dark Matter didn't survive by shaking hands with normal matter. Instead, it survived by interacting with its heavier twin ($\chi_2$).

The authors describe three ways this happens, using the analogy of a crowded dance floor:

1. Co-annihilation (The "Double Trouble"): The twins bump into each other and disappear together, leaving behind normal particles. This is the old, standard way.
2. Coscattering (The "Crowd Surf"): The heavy twin ($\chi_2$) bumps into a normal particle (like a photon or electron) and gets knocked down, turning into the light twin ($\chi_1$) in the process. It's like a surfer riding a wave to get to the shore.
3. Conversion (The "Magic Switch"): This is the star of the show. The heavy twin ($\chi_2$) bumps into another dark twin, and they swap identities. The heavy one becomes light, and the light one becomes heavy. This happens so efficiently that it keeps the right amount of Dark Matter in the universe without needing to talk to normal matter much.

The Two Scenarios: The "Resonance" and the "Secluded" Room

The paper tests this idea in two different "rooms" (scenarios) based on the weight of the messenger ($Z'$):

1. The Resonance Scenario (The "Perfect Echo")

• The Setup: The messenger ($Z'$) is very heavy, exactly twice the weight of the Dark Matter twins.
• The Result: This creates a "perfect echo" (resonance). It makes the interactions very efficient.
• The Catch: Because the messenger is so heavy, the "Conversion" mechanism works best here. However, the messenger is so heavy that current particle colliders can't easily see it. The only way to find this scenario might be to look for the heavy twin ($\chi_2$) decaying very slowly, which would leave a faint signal in the Cosmic Microwave Background (the afterglow of the Big Bang).

2. The Secluded Scenario (The "Private Party")

• The Setup: The messenger ($Z'$) is lighter than the Dark Matter twins.
• The Result: The twins can't talk to normal matter directly. Instead, they talk to each other and create more messengers ($Z'$).
• The Catch: This is actually the most promising place to look! Because the messenger is light, it's easier to create. The "Conversion" mechanism works very well here.
• The Discovery: In this scenario, the Dark Matter could be detected by:
  • Direct Detection: Hitting a detector with a "nudge" (if the twins are close enough in weight).
  • Indirect Detection: Seeing the messengers decay into light particles (like electrons) in space.
  • Cosmic Microwave Background: Seeing the long-lived heavy twin decay later in the universe's history.

The Conclusion: Why This Matters

The paper concludes that the old idea of Dark Matter just "shaking hands" with normal matter is in trouble because we haven't found it.

However, this new idea—where Dark Matter has a heavier twin and survives by switching identities (conversion)—is a very strong candidate.

• It explains why we haven't seen it yet (it's wearing a disguise).
• It predicts that the Conversion Mechanism is the most likely way Dark Matter was created.
• It suggests that the Secluded Scenario (where the messenger is light) is the most exciting place to look next, offering hope for detection by future telescopes and particle colliders.

In short: Dark Matter might not be a lonely ghost. It might be a shy person with a loud twin brother, and they are constantly swapping places to survive in our universe.

Technical Summary

Technical Summary: Reviving Z′ Portal Dark Matter with Conversion Mechanism

Problem Statement
In many new physics models featuring extended gauge symmetries, the $Z'$ boson serves as a mediator between Dark Matter (DM) and Standard Model (SM) particles. However, conventional $Z'$ portal DM scenarios face significant challenges: the gauge coupling required to reproduce the observed relic density is typically constrained to be very small by direct detection experiments (due to spin-independent scattering) and collider searches (due to $Z'$ production limits). While inelastic DM models with mass splitting offer a solution by kinematically suppressing scattering, traditional approaches often rely on coannihilation mechanisms that may not sufficiently alleviate these constraints or explore the full range of production dynamics. The authors aim to address these pressing issues by investigating a specific inelastic Dirac DM model within a gauged $U(1)_{B-L}$ framework, focusing on novel production mechanisms—specifically coscattering and conversion—that arise from a compressed mass spectrum.

Methodology
The study proposes a benchmark model extending the SM with a gauged $U(1)_{B-L}$ symmetry and two vector-like Dirac fermions, $\tilde{\chi}_1$ and $\tilde{\chi}_2$.

• Model Structure: $\tilde{\chi}_1$ is neutral under $U(1)_{B-L}$, while $\tilde{\chi}_2$ carries a non-zero charge $Q_{\tilde{\chi}_2}$. A dark scalar $\phi$ acquires a vacuum expectation value, inducing a mass mixing term $\delta m \bar{\tilde{\chi}}_1 \tilde{\chi}_2$. This results in mass eigenstates $\chi_1$ (the DM candidate) and $\chi_2$ (a heavier partner), related by a mixing angle $\theta$.
• Interaction Dynamics: The interaction between $\chi_1$ and the $Z'$ boson is suppressed by $\sin^2\theta$, leading to a small effective gauge coupling. The relic density is determined by solving coupled Boltzmann equations that include:
  • (Co)annihilation: $\chi_1 \bar{\chi}_1 \to f\bar{f}$, $\chi_2 \bar{\chi}_2 \to f\bar{f}$, and $\chi_1 \chi_2 \to f\bar{f}$.
  • Coscattering: $\chi_2 f \to \chi_1 f$.
  • Conversion: $\chi_2 \chi_i \to \chi_1 \chi_j$ (where $i,j \in \{1,2\}$).
  • Three-body decays: $\chi_2 \to \chi_1 f \bar{f}$.
• Scenarios: The analysis is divided into two regimes based on the mass ratio $r_{Z'} = m_{Z'}/m_{\chi_2}$:
  1. Resonance Scenario: $r_{Z'} \simeq 2$, where $Z'$ mediates annihilation near the resonance peak.
  2. Secluded Scenario: $m_{Z'} < m_{\chi_{1,2}}$, where the dominant process is $\chi_{1,2} \bar{\chi}_{1,2} \to Z' Z'$.
• Tools and Constraints: The authors utilize micrOMEGAs for numerical calculations of relic density and cross-sections. They systematically apply constraints from:
  • Colliders: LEP, LHCb, BaBar, CMS, ATLAS, and future projections (FCC-ee, Belle II).
  • Direct Detection: Current (PandaX-4T, LZ, DarkSide-50) and future (SuperCDMS, LZ) limits on spin-independent scattering.
  • Indirect Detection: Fermi-LAT, H.E.S.S., AMS, and CMB constraints on annihilation cross-sections.
  • Cosmology: Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) limits on long-lived $\chi_2$ decays.

Key Contributions

1. Extension of Inelastic DM: Unlike previous minimal inelastic Dirac DM studies (often restricted to the MeV scale with fixed charges), this work explores the GeV to TeV mass scale with $Q_{\tilde{\chi}_2}$ as a free parameter.
2. Identification of Dominant Mechanisms: The paper demonstrates that for a compressed spectrum ($m_{\chi_1} \simeq m_{\chi_2}$) and specific coupling ranges, the conversion mechanism ($\chi_2 \chi_i \to \chi_1 \chi_j$) and coscattering ($\chi_2 f \to \chi_1 f$) can dominate the relic density calculation, often superseding traditional coannihilation.
3. Phenomenological Mapping: The authors provide a comprehensive mapping of the viable parameter space ($m_{\chi_1}, \Delta_\chi, r_{Z'}, g', g_\chi, \theta$) under current and future experimental constraints for both resonance and secluded scenarios.

Results

• Resonance Scenario ($r_{Z'} \simeq 2$):

  • The conversion mechanism is favored in a region where $g' \sim \mathcal{O}(10^{-3})$ and $m_{Z'}$ ranges from GeV to TeV. This region is potentially accessible to future colliders (CMS, ATLAS, FCC-ee).
  • Coannihilation dominates at very small couplings ($g' \lesssim 10^{-5}$), leading to long-lived $\chi_2$. This regime is primarily probed by future CMB observations rather than direct detection or colliders.
  • Direct and indirect detection signals are generally suppressed by the small mixing angle $\theta$, making them challenging to observe unless $\theta$ is significantly larger than the benchmark values.
  • Coscattering is largely excluded by current collider constraints due to the requirement of larger $g'$.

• Secluded Scenario ($m_{Z'} < m_{\chi_{1,2}}$):

  • The conversion mechanism is robust and largely independent of $g'$ at low masses, making it a promising candidate for detection via indirect detection and CMB.
  • Coannihilation is largely excluded by current $Z'$ constraints for large $g'$.
  • Coscattering is viable for $g' \sim \mathcal{O}(10^{-4})$ and is accessible to future direct detection experiments (if $\Delta_\chi$ and $g_\chi$ are favorable) and colliders.
  • The secluded scenario allows for larger mixing angles ($\theta \sim \mathcal{O}(10^{-3})$) compared to the resonance case, enhancing the prospects for direct and indirect detection.

• Long-lived Particles: In both scenarios, specific parameter choices lead to long-lived $\chi_2$ particles. The paper identifies regions where $\chi_2$ decays affect BBN and CMB anisotropies, providing a complementary probe to collider searches.

Significance and Claims
The paper claims that the conversion mechanism is a viable and favored pathway for $Z'$ portal dark matter under current constraints, particularly in both resonance and secluded scenarios. The authors argue that this mechanism allows for viable parameter spaces that are often inaccessible to traditional coannihilation models or are more robust against direct detection limits due to the suppressed effective coupling.

The study highlights that:

1. The conversion mechanism offers a distinct phenomenological signature where the relic density is determined by inelastic conversions with a heavier dark partner, relaxing the stringent requirements on the gauge coupling and mixing angle.
2. The secluded scenario presents a more promising landscape for future experimental tests compared to the resonance scenario, particularly for direct and indirect detection, due to the ability to accommodate larger mixing angles.
3. Future CMB observations play a critical role in probing the low-coupling, long-lived $\chi_2$ regimes that are beyond the reach of current and planned colliders.

The authors conclude that while the resonance scenario faces challenges from collider constraints on coscattering, the secluded scenario, driven by conversion and specific coannihilation regions, offers a robust framework for reviving $Z'$ portal dark matter with testable signatures in upcoming experiments.