Vector-like dark matter within an alternative left-right symmetric model

This paper proposes a viable TeV-scale vector-like dark matter candidate within an extended left-right symmetric model featuring an additional $SU(2)$ gauge symmetry, demonstrating its consistency with relic abundance, collider limits, and current direct and indirect detection constraints while highlighting the complementary roles of future multi-ton detectors and the CTA telescope in probing the model's parameter space.

The Gist

Imagine the universe is a giant, bustling city. We know a lot about the people living in the "Visible District" (the Standard Model of physics)—the stars, planets, and atoms that make up everything we see. But we also know there's a massive, invisible "Dark Sector" that makes up about 85% of the city's population. We can't see them, but we know they're there because their gravity holds the city together. We call this invisible population Dark Matter.

For decades, physicists have been trying to figure out who these invisible neighbors are. This paper proposes a new theory about a specific type of Dark Matter candidate, using a clever twist on an existing architectural blueprint of the universe.

Here is the story of their discovery, explained simply:

1. The Blueprint: A City with Two Sides

The authors start with a famous blueprint called the Left-Right Symmetric Model (LRSM). Think of this as a city designed with perfect symmetry: a "Left Side" and a "Right Side." In our current understanding of physics, the "Left Side" (where our familiar particles live) behaves differently than the "Right Side." This model tries to fix that imbalance, suggesting that at high energies, the two sides were once mirror images of each other.

However, this blueprint had a flaw: it didn't have a place for a stable Dark Matter resident. It was like a city plan that accounted for all the houses but forgot to build a park for the invisible population.

2. The New Residents: Vector-Like Leptons

To fix this, the authors add a new neighborhood to the city: a Vector-Like Lepton (VLL) district.

• What are they? Imagine a new family of particles. Unlike our normal particles, which have a specific "handedness" (like being left-handed or right-handed), these new particles are "ambidextrous." They are Vector-Like, meaning they can interact with the forces of the universe in a balanced way.
• The Dark Matter Candidate: This new family has a neutral member (let's call him N) and a charged member (let's call her E). The authors propose that N is the Dark Matter. He is invisible, stable, and heavy (weighing as much as a small mountain, or a few thousand times the mass of a proton).

3. The Security Guard: The Parity Symmetry

A major problem in physics is: Why doesn't Dark Matter mix with normal matter and decay? If it did, it wouldn't last long enough to be the Dark Matter we see today.

Usually, scientists put up a "Do Not Enter" sign (a $Z_2$ symmetry) to keep them separate. But in this specific city blueprint, that sign wouldn't work because of how the roads (interactions) are built.

So, the authors invent a new security rule: Parity Symmetry.

• The Analogy: Imagine a strict bouncer at the club of the Dark Sector. The bouncer has a rule: "No mixing allowed between the VIPs (Vector-Like Leptons) and the regular guests (Standard Model particles)."
• The Result: Because of this rule, our Dark Matter candidate N cannot turn into normal particles. He is locked in the Dark Sector, safe and stable for billions of years. He can only talk to the visible world through two specific "gates":
  1. The Vector Portal: Exchanging heavy force-carrying particles (like heavy versions of the W and Z bosons).
  2. The Lepton Portal: Swapping with his charged partner E.

4. The Detective Work: Hunting for the Ghost

The authors then played the role of detectives, checking if this new candidate fits the clues we already have:

• The Weight Limit (Relic Abundance): We know exactly how much Dark Matter exists in the universe (measured by the Planck satellite). The authors calculated that for N to have the right amount, he needs to be very heavy—around the TeV scale (a trillion electron volts). This is like saying the Dark Matter resident is a giant, not a dwarf.
• The Collider Constraints (The LHC): The Large Hadron Collider (LHC) is like a giant crash-test facility where scientists smash particles to see what breaks. The authors checked: "If we smash particles hard enough, would we have already seen these new heavy particles?"
  • The Verdict: If Dark Matter were light (like the weight of a human), we would have seen it by now. Since we haven't, the Dark Matter must be heavy (TeV scale).
• The Direct Detection (LZ Experiment): The LUX-ZEPLIN (LZ) experiment is a giant tank of liquid xenon deep underground, waiting for a Dark Matter particle to bump into an atom.
  • The Verdict: The authors found that if Dark Matter is too light, it would have already bumped into the xenon atoms and been detected. Since it hasn't, the "light" candidates are ruled out. The heavy candidates (TeV scale) are just barely hiding from the current detectors, but they are right on the edge of being found.

5. The Future: Complementarity

The paper concludes with a hopeful message about how we will find them. It uses a great analogy of Direct vs. Indirect Detection:

• Direct Detection (XLZD): Imagine trying to catch a thief by setting a trap in their house. Future, even bigger tanks (like XLZD) might finally catch a bump from our heavy Dark Matter candidate.
• Indirect Detection (CTA): Imagine trying to find the thief by looking for the smoke from the fire they started. If two Dark Matter particles collide and annihilate, they might release gamma rays. The Cherenkov Telescope Array (CTA) is a giant eye in the sky looking for this "smoke."

The Big Takeaway:
The authors show that these two methods are complementary.

• If the Dark Matter is just below the detection limit of the giant xenon tanks, the telescope (CTA) might see the gamma rays from their collisions.
• If the telescope sees nothing, the xenon tanks might still catch a bump.

Summary

In simple terms, this paper says:
"We have a new theory about the universe that adds a heavy, invisible, 'ambidextrous' particle to the mix. We've proven that this particle is stable because of a new 'no-mixing' rule. It's too heavy to be the light Dark Matter we ruled out, but it's the perfect candidate for the heavy Dark Matter we are looking for. It's currently hiding just out of reach of our current detectors, but the next generation of giant tanks and space telescopes will likely catch it."

It's a story of a new suspect in the mystery of the universe, one that fits the clues perfectly and is waiting to be caught by our best technology.

Technical Summary

Here is a detailed technical summary of the paper "Vector-like dark matter within an alternative left-right symmetric model" by Bouzeraib, Zidi, and Bélanger.

1. Problem Statement

The standard Left-Right Symmetric Model (LRSM) is a well-established extension of the Standard Model (SM) designed to explain parity violation and neutrino masses via the seesaw mechanism. However, the minimal LRSM does not naturally provide a viable Dark Matter (DM) candidate. Previous attempts to incorporate DM into LRSM frameworks (e.g., light right-handed neutrinos or scalar triplets) have faced issues regarding naturalness, relic density reproduction, or stability.

This paper addresses the problem of identifying a stable, viable DM candidate within an extended LRSM framework that includes:

• An additional non-abelian $SU(2)_V$ gauge symmetry.
• One generation of Vector-Like Leptons (VLLs) transforming under the fundamental representation of $SU(2)_V$.
• A mechanism to ensure the stability of the neutral VLL component without relying on ad-hoc discrete symmetries that conflict with the model's Yukawa structure.

2. Methodology and Model Construction

Model Framework

The authors extend the gauge group to $SU(2)_V \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$.

• Particle Content: The model introduces a vector-like lepton doublet $L_{L,R} = (N, E^\pm)^T$ charged under $SU(2)_V$. $N$ is the neutral DM candidate, and $E^\pm$ is its charged partner.
• Symmetry Breaking: The symmetry breaking hierarchy is defined as $SU(2)_V \xrightarrow{u_R} SU(2)_L \times SU(2)_R \xrightarrow{v_R} SU(2)_L \times U(1)_Y \xrightarrow{v_{EW}} U(1)_{EM}$. The VLLs acquire mass through a self-dual bi-doublet scalar $\Phi_{VR}$ with a vacuum expectation value (vev) $u_R$ at the TeV scale.
• Stability Mechanism: To stabilize the DM candidate $N$, the authors impose a discrete parity symmetry that forbids mixing between the VLLs and chiral SM leptons. This sets the Yukawa couplings ($\lambda_l, \lambda'_l$) to zero. Consequently, the dark sector interacts with the visible sector exclusively through:
  1. Vector Portal: $s$-channel processes mediated by neutral ($Z', Z''$) and charged ($W', W''$) gauge bosons.
  2. VLL Portal: $t$-channel processes mediated by the VLLs themselves.

Computational Approach

• Tools: The model was implemented using FeynRules and exported to CalcHEP. Dark matter observables (relic density, scattering cross-sections) were calculated using micrOMEGAs.
• Constraints: The analysis incorporates:
  • Collider Limits: LHC constraints on $W'$ mass (via $N_2 \mu^\pm$ channels) and LEP constraints on charged lepton masses ($E^\pm$).
  • Direct Detection (DD): Limits from the LZ (LUX-ZEPLIN) experiment and projections for XLZD.
  • Indirect Detection (ID): Constraints from Fermi-LAT (dwarf spheroidal galaxies) and projections for the CTA (Cherenkov Telescope Array).
• Parameter Scan: A general scan was performed over four free parameters: the gauge coupling $g_V$, the $W'$ mass ($m_{W'}$), the DM mass ($m_N$), and the mass splitting $\Delta m = m_E - m_N$.

3. Key Contributions

1. Novel Stability Mechanism: The paper proposes a specific parity symmetry to stabilize the VLL DM candidate, overcoming the incompatibility of standard $Z_2$ symmetries with the required scalar sector structure for VLL mixing.
2. Interaction Topology: It establishes that in this specific model, DM-nucleon scattering is purely mediated by vector bosons ($Z, Z', Z''$) via $t$-channel diagrams, with no Higgs-mediated contributions due to the chargeless nature of the bi-doublet under $SU(2)_V$.
3. Complementarity of Probes: The study rigorously demonstrates the complementarity between Direct Detection (DD) and Indirect Detection (ID) experiments, particularly for TeV-scale DM where DD experiments may hit the "neutrino floor."

4. Key Results

Relic Density and Mass Scales

• Resonance Requirement: To satisfy the observed relic density ($\Omega h^2 \approx 0.12$), the DM mass $m_N$ must generally lie near the resonance of the mediator masses ($m_N \approx m_{Z'}/2$ or $m_{Z''}/2$).
• Mass Splitting Scenarios:
  • Large Splitting ($\Delta m \sim 1$ TeV): Relic density is determined by $s$-channel annihilation via $Z'/Z''$.
  • Small Splitting ($\Delta m \sim 1$ GeV): Co-annihilation with $E^\pm$ becomes dominant. However, this scenario is heavily constrained by collider searches.

Collider Constraints

• Low Mass Exclusion: Points with $m_N < 104$ GeV are excluded by LEP (chargino searches) and LEP1 ($Z$-width constraints).
• Electroweak Scale: Points with $m_N \sim 130$ GeV (requiring small $\Delta m$) survive LHC long-lived particle searches but are completely excluded by LZ direct detection limits.
• TeV Scale: Viable DM exists at the TeV scale ($m_N > 1.5$ TeV).

Direct Detection (DD)

• Cross-Section Behavior: The spin-independent (SI) scattering cross-section is dominated by $Z'$ and $Z''$ exchange. The interference between $Z, Z', Z''$ contributions leads to complex behavior where the cross-section can be suppressed for specific values of $g_V$.
• Current Limits: Current LZ limits exclude a significant portion of the parameter space, particularly for lighter gauge boson masses.
• Future Projections: Future multi-ton experiments like XLZD will probe most of the remaining viable parameter space, though some points may fall below the "neutrino floor."

Indirect Detection (ID)

• Fermi-LAT: Current limits from dwarf spheroidal galaxies do not constrain the TeV-scale DM in this model.
• CTA Prospects: The CTA telescope offers a unique probe. The paper finds that a significant fraction of the TeV-scale parameter space (specifically points where DM is under-abundant, $\xi \ll 1$, but has high annihilation cross-sections) is within the reach of CTA.
• Complementarity: CTA can probe regions of parameter space that are inaccessible to next-generation DD experiments (e.g., points below the neutrino floor or those with suppressed scattering cross-sections but efficient annihilation).

5. Significance and Conclusion

This work demonstrates that an extended LRSM with vector-like leptons provides a theoretically consistent and phenomenologically viable Dark Matter candidate. The key findings are:

• Viability: The model successfully explains the DM relic density with a TeV-scale neutral vector-like lepton.
• Exclusion of Low Mass: The model effectively rules out the electroweak scale for this specific DM candidate due to the tight interplay between co-annihilation requirements and collider/DD constraints.
• Future Outlook: The survival of the model relies on the TeV scale. The study highlights a critical complementarity: while direct detection experiments (XLZD) will test the majority of the parameter space, the CTA telescope is essential for probing the remaining "blind spots," particularly those with suppressed scattering cross-sections or those falling below the neutrino floor.

The authors conclude that while simplifying assumptions were made (e.g., decoupled scalars, fixed heavy neutrino masses), the core result—that vector-like leptons in an extended LRSM offer a testable DM scenario accessible to future multi-messenger experiments—remains robust.