A Common Origin of Asymmetric Self-interacting Dark Matter and Dirac Leptogenesis

Assuming dark matter to be asymmetric as well as self-interacting and neutrinos to be Dirac fermions, we propose a framework to address the observed baryon imbalance of the universe. We add three right-handed neutrinos $ν_{R_i},,{i=1,2,3}$, one singlet fermion $χ$, a doublet fermion $ψ$, and heavy scalar doublets $η_i,,{i=1,2}$ to the Standard Model. A global $B-L$ is imposed to protect the Dirac nature of neutrinos. Both $χ$ and $ψ$ are fermions with non-zero charge under an extended $U(1)_{B-L} \times U(1)_D$ symmetry. Additionally, a $\mathcal{Z}_2$ symmetry is imposed, where the singlets $χ$, $ν_R$, and $η$ are negative and the doublet $ψ$ is positive. The CP-violating out-of-equilibrium decay of heavy scalar $η$ generates an equal and opposite $B-L$ asymmetry among the left-handed ($ν_L$) and right-handed ($ν_R$) neutrinos. The $ν_L-ν_R$ equilibration process does not take place until below the Electroweak phase transition scale because of tiny Yukawa couplings. During this time, Sphaleron processes, which are active at temperatures higher than 100 GeV, transform a portion of the $B-L$ asymmetry stored in left-handed neutrinos into baryon asymmetry. MeV scale gauge boson $Z’$ of $U(1)_D$ sector mediates both annihilation of symmetric dark matter component and self-interaction among dark matter particles. Moreover, $Z’$ mixes with the Standard Model Z-boson and provides a portal for dark matter direct detection.

💡 Research Summary

The paper proposes a unified framework that simultaneously accounts for the observed baryon asymmetry of the Universe and the relic abundance of self‑interacting asymmetric dark matter (SIDM), while keeping neutrinos as Dirac particles. The particle content is extended by three right‑handed neutrinos (ν_R), a singlet fermion χ, a doublet fermion ψ, and two heavy scalar doublets η₁, η₂. A global U(1)_{B‑L} symmetry is imposed to forbid Majorana masses and protect the Dirac nature of neutrinos, and a discrete Z₂ symmetry makes η, ν_R and χ odd while ψ and all Standard Model (SM) fields are even. Both ψ and χ carry charges under an additional gauge group U(1)_D; the associated gauge boson Z′ has a mass in the MeV range.

The core mechanism for baryogenesis is “Dirac leptogenesis”. The heavy scalars η are in thermal equilibrium in the early Universe and decay out of equilibrium when the temperature drops below their mass. Their decays proceed through two channels: η → ℓ ν_R (visible sector) and η → ψ χ (dark sector). Because two copies of η are introduced, CP‑violating interference between tree‑level and self‑energy one‑loop diagrams generates a CP asymmetry ε_L. This asymmetry creates equal and opposite B‑L charges in left‑handed (ν_L) and right‑handed (ν_R) neutrinos. Sphaleron processes, active above ≈100 GeV, convert the left‑handed lepton asymmetry into a baryon asymmetry, while the right‑handed asymmetry remains untouched until after the electroweak phase transition (EWPT) because the Yukawa couplings linking ν_L and ν_R are tiny (y ≈ 10⁻¹²). Consequently, the generated baryon asymmetry is Y_B ≈ −0.55 Y_L, which can reproduce the observed value η_B ≈ 6 × 10⁻¹⁰ for reasonable choices of parameters (M_η ≈ 10¹⁰ GeV, f ≈ 10⁻⁴, λ ≈ 10⁻⁷).

Neutrino Dirac masses arise from a soft Z₂‑breaking term μ² η†H. After integrating out η, a one‑loop diagram yields M_ν ≈ f ⟨H⟩ μ²/M_η². With μ/M_η ≈ 10⁻⁴ and f ≈ 10⁻⁴, neutrino masses of order 0.1 eV are obtained, consistent with oscillation data.

In the dark sector, ψ remains in equilibrium via its SU(2)_L interactions, while χ, being a SM singlet, attains equilibrium through the U(1)D gauge interaction mediated by Z′. The same interaction also enables efficient annihilation of the symmetric component χ χ → Z′ Z′. The thermally averaged cross‑section ⟨σv⟩ ≈ π α′² M_χ²/(M_χ² − M{Z′}²)², with α′ = g′²/4π and g′ ≈ 0.1, is two orders of magnitude larger than the canonical freeze‑out value, ensuring that the symmetric relic is negligible. The remaining dark matter density is therefore dominated by the asymmetric χ population generated together with the baryon asymmetry in the η decays.

The light Z′ simultaneously provides the required self‑interaction for SIDM. For M_{Z′} ≈ 10 MeV and g′ ≈ 0.1, the self‑scattering cross‑section per unit mass is σ/m ≈ 1 cm²/g, a value that can alleviate small‑scale structure issues (core‑cusp, missing satellites, too‑big‑to‑fail). Kinetic mixing between Z′ and the SM Z boson, parameterized by ε ≲ 10⁻⁸, opens a portal for direct detection. This mixing is small enough to evade current bounds from beam‑dump, fixed‑target, and collider experiments, yet large enough to give detectable nuclear recoil rates in upcoming low‑threshold detectors.

The authors discuss the theoretical robustness of the global B‑L symmetry, noting that quantum‑gravity effects could violate global symmetries. They argue that gauging B‑L resolves this issue; the charge assignments already cancel anomalies, and the additional gauge boson can be made heavy (M_{Z_{B‑L}} ≫ TeV) so that low‑energy phenomenology is unchanged. A scalar ϕ_{B‑L} could break the gauge symmetry at a high scale without inducing unwanted Majorana mass terms.

Phenomenological constraints are examined qualitatively. The MeV Z′ contributes to ΔN_eff during BBN and CMB epochs; with g′ ≈ 0.1 the contribution stays within the current bound ΔN_eff ≲ 0.3. The small kinetic mixing satisfies limits from electroweak precision tests and direct detection experiments. Collider signatures involve production of ψ ψ or χ χ pairs via off‑shell Z′, leading to missing‑energy signatures, but the rates are suppressed by the tiny ε. Future lepton colliders or dedicated fixed‑target experiments could probe the kinetic mixing region.

In summary, the paper presents a coherent model where the out‑of‑equilibrium decay of heavy scalar doublets simultaneously generates (i) a Dirac neutrino mass, (ii) a baryon asymmetry via Dirac leptogenesis, and (iii) an asymmetric dark matter relic with the correct self‑interaction strength. The framework ties together three major open questions—neutrino nature, baryogenesis, and small‑scale structure—while remaining compatible with existing cosmological and laboratory constraints. Nonetheless, the reliance on a global B‑L symmetry (or its gauged version), the need for finely tuned parameters (μ/M_η, tiny Yukawas), and the limited discussion of detailed parameter scans and wash‑out processes suggest that further quantitative studies are required to fully establish the viability of the scenario.