Leptogenesis and Dark Matter in an Inverse Seesaw from gauged B-L breaking

We study a dynamical realization of the low-scale Inverse Seesaw mechanism in which the approximate $B-L$ symmetry is gauged and spontaneously broken. Anomaly cancellation requires additional chiral fermions, one of which becomes a stable dark matter candidate after symmetry breaking, while another remains massless and contributes to dark radiation. Focusing on the regime of feeble gauge interactions, we compute the dark matter relic abundance produced via the freeze-in mechanism through the $B-L$ gauge boson and identify the parameter space consistent with cosmological and laboratory constraints. We show that the same region naturally avoids thermalization of heavy neutral leptons, preserving the viability of ARS leptogenesis. The interplay between dark matter production, dark radiation constraints, and leptogenesis requirements leads to a predictive scenario where future cosmological surveys and intensity-frontier experiments such as SHiP can probe significant portions of the viable parameter space.

💡 Research Summary

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The paper presents a comprehensive framework that embeds a low‑scale Inverse Seesaw (ISS) mechanism into a gauged U(1)_{B‑L} symmetry which is broken spontaneously. To cancel the B‑L gauge anomalies, three additional chiral fermions are introduced: a pair χ_R, χ_L that combine into a Dirac fermion χ and a singlet ω that remains massless. The χ field is automatically stable because the charge assignment leaves an accidental global “dark‑matter number” conserved after symmetry breaking, making χ a natural dark‑matter (DM) candidate. The massless ω contributes one extra relativistic degree of freedom, thereby affecting the effective number of neutrino species N_{eff}.

The scalar sector contains two complex singlets ϕ₁ (B‑L charge +1) and ϕ₂ (charge +2). The vacuum expectation value (VEV) of ϕ₁, v₁, generates the Dirac mass of χ (m_χ = y_χ v₁/√2). The VEV of ϕ₂, v₂, is induced through a cubic coupling η ϕ₁² ϕ₂† and is naturally suppressed (v₂ ≈ √2 η v₁²/m₂²). This small v₂ yields a tiny Majorana mass μ = y_N v₂/√2 for the right‑handed neutrinos N_R, N′_R, which is the source of lepton‑number violation in the ISS. Consequently, active neutrino masses arise as m_ν ≈ (v²/2) y_ν M_N⁻¹ μ M_N⁻ᵀ y_νᵀ, with μ naturally small without fine‑tuning, satisfying the technical naturalness criterion.

The B‑L gauge boson Z′ acquires a mass m_{Z′}=g_{B‑L} v₁. The authors focus on a feeble gauge coupling g_{B‑L} ≈ 10⁻⁷ and a Z′ mass of a few GeV, which makes Z′ a “dark” mediator: it couples to SM fermions via the B‑L current but its interactions are weak enough to avoid thermal equilibrium between the dark sector and the SM plasma. This regime is essential for the freeze‑in production of χ, ensuring that the heavy neutral leptons (HNLs) remain out of equilibrium, a prerequisite for successful Akhmedov‑Rubakov‑Smirnov (ARS) leptogenesis.

Dark‑matter production is studied through a set of coupled Boltzmann equations for the comoving yields Y_{DM}, Y_{Z′}, and Y_ω. The dominant freeze‑in channels are χ χ̄ → SM fermion pairs (via off‑shell Z′), χ χ̄ → Z′ Z′ (if kinematically allowed), and χ χ̄ → ω ω̄. The authors assume an initial negligible abundance after reheating (T_R = 100 m_χ) and solve the equations analytically in the limit g_{B‑L} ≲ 10⁻⁸, where Z′ never thermalizes. They find that the observed DM relic density Ω_{DM} h² ≈ 0.12 can be reproduced for χ masses in the TeV range, Yukawa coupling y_χ ≈ 10⁻³ (comparable to the muon Yukawa), and g_{B‑L} ≈ 10⁻⁹–10⁻⁷. Larger gauge couplings would bring Z′ into equilibrium, leading to overproduction of χ and ω, thereby violating the freeze‑in assumption.

The massless ω contributes ΔN_{eff} ≈ 0.1–0.5 depending on the exact thermal history. Current Planck+BAO limits (ΔN_{eff} ≲ 0.3) therefore impose a lower bound on the symmetry‑breaking scale v₁ ≈ 10⁴ TeV, which simultaneously ensures m_{Z′} ≈ few GeV and suppresses ω production. This bound is compatible with the gauge‑coupling range required for freeze‑in.

For leptogenesis, the authors adopt the ARS mechanism, which relies on CP‑violating oscillations of HNLs with masses 1–100 GeV. The small μ term generated by v₂ guarantees that the active‑sterile mixing θ ≈ v y_ν/(√2 M_N) can be kept at 10⁻⁵–10⁻⁶, preventing the HNLs from equilibrating before the electroweak sphaleron freeze‑out. The HNL lifetimes are required to be τ_N ≲ 10⁻² s to avoid conflicts with Big‑Bang Nucleosynthesis. Within the chosen parameter space, the authors demonstrate that sufficient lepton asymmetry can be generated and subsequently converted into the observed baryon asymmetry.

The phenomenological implications are explored in detail. The Z′ boson, with a mass of a few GeV and a tiny coupling, lies within the reach of current and upcoming intensity‑frontier experiments such as NA62, LHCb, and especially the proposed SHiP experiment, which can probe displaced‑vertex signatures from Z′ → ℓ⁺ℓ⁻ decays. Direct detection of χ is highly suppressed due to the feeble gauge coupling, but indirect signals may arise from Z′ decays in fixed‑target setups. Future CMB‑Stage‑4 measurements of N_{eff} will further test the presence of the massless ω. The authors present a combined exclusion plot showing the viable region after imposing dark‑matter relic density, ΔN_{eff}, HNL decay, and existing Z′ searches.

In summary, the paper constructs a self‑consistent, predictive model where a gauged B‑L symmetry simultaneously explains tiny neutrino masses via a low‑scale Inverse Seesaw, provides a viable freeze‑in dark‑matter candidate, yields a controllable contribution to dark radiation, and preserves the conditions for ARS leptogenesis. The allowed parameter space is narrow but testable with near‑future intensity‑frontier experiments and precision cosmology, offering a compelling target for both particle‑physics and astrophysical searches.