Leptogenesis from Dark Matter Coannihilation

1. Problem Statement

The paper addresses two major unsolved problems in particle physics and cosmology:

1. Dark Matter (DM): The Standard Model (SM) lacks a viable candidate for the observed non-baryonic dark matter, which constitutes $\Omega_{DM}h^2 \approx 0.12$.
2. Baryon Asymmetry of the Universe (BAU): The observed matter-antimatter asymmetry ($\eta_B \approx 6 \times 10^{-10}$) cannot be explained by the SM due to insufficient CP violation and a weak electroweak phase transition.

While WIMPy Leptogenesis (where DM annihilation generates lepton asymmetry) is a known concept, standard Type-I Seesaw Leptogenesis typically requires heavy Right-Handed Neutrinos (RHNs) with masses $M_1 \gtrsim 10^9$ GeV (Davidson-Ibarra bound) to generate sufficient CP asymmetry, making the mechanism untestable at current colliders. The authors aim to construct a minimal, testable model where:

• Leptogenesis occurs at the TeV scale.
• The generation of BAU is directly linked to the coannihilation of Dark Matter and its heavier partners, rather than just DM annihilation or RHN decay.
• The model remains consistent with light neutrino mass data.

2. Methodology and Model Construction

Model Extension

The authors propose a minimal extension of the Type-I Seesaw model by introducing three new singlet fields under the SM gauge group, augmented by a discrete $Z_2$ symmetry:

• $N_{1,2}$: Two singlet fermions (Right-Handed Neutrinos).
• $\psi$: A singlet fermion (odd under $Z_2$).
• $\phi$: A singlet scalar (odd under $Z_2$). This is the Dark Matter candidate.
• $\eta$: A singlet scalar (even under $Z_2$). This acts as a portal to ensure the correct DM relic density.

Key Interactions:

• Neutrino Mass: Generated via the standard Type-I seesaw mechanism involving $N_{1,2}$ and the SM Higgs doublet $H$.
• Dark Sector: The $Z_2$-odd particles ($\phi, \psi$) interact via the Yukawa coupling $y_i \bar{\psi}^c N_i \phi$.
• DM Relic Control: The $Z_2$-even scalar $\eta$ couples to $\phi$ via terms like $\mu_\eta \phi^2 \eta$ and $\lambda_{\eta\phi} \eta^2 \phi^2$. This allows the process $\phi\phi \to \eta\eta$ to dominate DM freeze-out after the lepton asymmetry is generated, ensuring the correct relic abundance without over-washing out the asymmetry.

The Mechanism: Coannihilation-Driven Leptogenesis

Unlike standard scenarios where RHN decay dominates, the lepton asymmetry here is dominantly generated by the coannihilation process $\phi \psi \to L H$ (and its CP-conjugate).

• CP Violation Sources:
  1. CP phases in the Dirac Yukawa couplings ($h_{\alpha i}$) of the neutrino sector.
  2. CP phases in the dark sector Yukawa couplings ($y_i$).
• Dynamics: The coannihilation process $\phi \psi \to L H$ occurs out of thermal equilibrium. The interference between tree-level and one-loop diagrams (self-energy and vertex corrections involving $N_{1,2}$) generates a net lepton asymmetry.
• Boltzmann Equations: The authors solve a coupled system of Boltzmann equations for the comoving number densities of $N_1$, $\psi$, $\phi$, and $B-L$. This tracks the evolution of the asymmetry from the early universe down to the sphaleron decoupling temperature ($T_{sph} \approx 131.7$ GeV).

3. Key Contributions

1. TeV-Scale Leptogenesis via Coannihilation: The paper demonstrates that successful leptogenesis can occur at the TeV scale ($M_1 \sim \mathcal{O}(10)$ TeV), bypassing the Davidson-Ibarra bound. This is achieved because the CP asymmetry is enhanced by the additional Yukawa couplings ($y_i$) connecting the dark sector to the RHNs, which are not constrained by light neutrino data in the same way the standard seesaw couplings are.
2. Minimal Realization: The model requires only two RHNs and two additional singlet scalars/fermions, making it a minimal extension of the Type-I seesaw.
3. Decoupling of Scales: The introduction of the $Z_2$-even scalar $\eta$ allows the DM relic density to be set by $\phi\phi \to \eta\eta$ annihilation at a temperature lower than the coannihilation freeze-out. This ensures that the DM abundance is correct without interfering with the earlier generation of lepton asymmetry.
4. CP Phase Independence: The model shows that successful leptogenesis is possible even if the standard Type-I seesaw CP violation vanishes at the one-loop level, provided there are CP-violating phases in the dark sector couplings ($y_i$).

4. Results and Numerical Analysis

The authors performed numerical scans using FeynRules, CalcHEP, and micrOMEGAs, solving the Boltzmann equations to identify viable parameter spaces.

• Parameter Space:
  • Masses: Successful scenarios are found with DM mass $m_\phi \sim 2\text{--}5$ TeV, partner mass $m_\psi \sim m_\phi + 1$ TeV, and RHN masses $M_1 \sim m_\phi + m_\psi$ (up to $\sim 11$ TeV).
  • Mass Splitting: A small mass splitting between RHNs ($\Delta M_{21} = M_2 - M_1 \sim 100$ GeV to 1 TeV) enhances the CP asymmetry via self-energy corrections, though resonant tuning (keV scale) is not required.
  • Couplings: Yukawa couplings $y_1, y_2$ in the range $0.01 \text{--} 1$ are required. Larger couplings enhance asymmetry but risk washout; an optimal window exists.
• Evolution of Asymmetry:
  • The coannihilation process $\phi \psi \to LH$ freezes out before the sphaleron decoupling, generating a $B-L$ asymmetry of $\sim 10^{-10}$, which converts to the observed baryon asymmetry.
  • The contribution from standard RHN decay ($N_1 \to LH$) is sub-dominant or washed out in this specific parameter regime.
• Direct Detection:
  • DM interacts with nuclei via Higgs portal mixing (between SM Higgs and $\eta$).
  • For $m_\phi > 3$ TeV, the spin-independent scattering cross-section ($\sigma_{SI}$) is currently allowed by LUX-ZEPLIN (LZ) and XENONnT but is within the sensitivity reach of future experiments like DARWIN.
• Indirect Detection:
  • DM annihilation into SM fermions ($\tau\bar{\tau}, b\bar{b}, t\bar{t}$) and gauge bosons ($W^+W^-$) is constrained by Fermi-LAT and HESS.
  • Resonant enhancement occurs if $m_\eta \approx 2m_\phi$. The authors show that for non-resonant masses or specific coupling ranges, the model evades current gamma-ray limits but remains testable by CTA and SWGO.

5. Significance and Conclusion

• Testability: The most significant outcome is that this mechanism brings leptogenesis down to the TeV scale, making it potentially testable at the LHC (via RHN production in specific textures) and future colliders, unlike the high-scale seesaw.
• Unified Origin: It provides an elegant, unified explanation for the origin of neutrino masses, the baryon asymmetry, and the dark matter abundance within a single minimal framework.
• Novelty: It shifts the paradigm from "RHN decay drives leptogenesis" to "Dark Sector coannihilation drives leptogenesis," offering a new pathway to satisfy the Sakharov conditions at low energies.
• Robustness: The model is robust against washout processes because the DM coannihilation freeze-out happens at a higher temperature than the DM self-annihilation freeze-out, ensuring the asymmetry is preserved.

In summary, the paper presents a viable, minimal, and testable scenario where the coannihilation of a TeV-scale Dark Matter particle and its partner generates the universe's matter-antimatter asymmetry, linking the dark sector directly to the origin of neutrino mass and baryogenesis.