Spontaneous Scoto-leptogenesis

The paper proposes a low-scale spontaneous leptogenesis scenario within the dynamical minimal scotogenic model, dubbed Spontaneous Scoto-leptogenesis, which simultaneously accommodates neutrino masses, inert scalar dark matter (DM), and the observed baryon asymmetry of the Universe (BAU). The mechanism relies on a rolling Majoron field arising from the spontaneous breaking of a global U(1) B-L symmetry, which induces an effective chemical potential for the B-L charge. This bias, combined with B-L-violating decays and inverse decays of right-handed neutrinos (RHNs), generates the baryon asymmetry via electroweak sphaleron conversion.

The paper states: "We propose a low-scale spontaneous leptogenesis scenario within the dynamical minimal scotogenic model for accommodating neutrino masses and inert scalar dark matter simultaneously. Thus, we dub the mechanism Spontaneous Scoto-leptogenesis. In this setup, a rolling Majoron arising from the global U(1) B-L symmetry breaking induces an effective chemical potential for the B-L charge in the presence of B-L violating interactions that allow for the efficient decays and inverse decays of right handed neutrinos (RHN), so it gives rise to the observed baryon asymmetry of the Universe through the electroweak sphaleron conversion."

The mechanism is shown to be effective in the strong washout regime, which is a key advantage over conventional thermal leptogenesis. The paper notes: "The mechanism becomes effective in the strong washout regime and successfully lowers the viable mass scale of the lightest RHN to the range of TeV scales, thereby making the thermal scotogenic leptogenesis with two hierarchical RHNs accessible to direct tests." Specifically, the observed baryon asymmetry can be generated with RHN masses as low as M1 = O(600) GeV, in sharp contrast to the conventional thermal leptogenesis lower bound of M1 ≳ 10 11 GeV.

The paper identifies the crucial role of the λ5 coupling, which controls both the mass splitting between the CP-even and CP-odd neutral inert scalars and the radiative neutrino mass generation. The paper states: We identify the roles of the λ5 coupling for spontaneous leptogenesis and inert scalar dark matter through the efficient erasure of the inert scalar asymmetry. The λ5-mediated interaction (η†Φ) squared determines whether a DM asymmetry survives and influences the spectator relations that convert the Majoron-induced charge density into the final baryon asymmetry.

The paper also explores the possibility of Majoron DM from kinetic misalignment, showing that a multicomponent dark sector comprising the inert scalar and the Majoron can be realized. The paper states: We also explore the regime for Majoron dark matter from the kinetic misalignment, showing that a multicomponent dark sector comprising the inert scalar and the Majoron can be realized in the model.

The framework provides a unified origin for low-scale baryogenesis, neutrino masses, and a multicomponent dark sector, testable through complementary experimental probes: "The resulting framework provides a unified origin for low-scale baryogenesis, neutrino masses, and multicomponent dark sector, so it can be tested by complementary experimental probes through direct detection experiments, collider searches for inert scalars, and future detection of Majoron dark matter or dark radiation."

The paper details the model setup: the scotogenic model is extended with a complex scalar field φ (SM singlet) carrying U(1) B-L charge 2 and Z2 charge +, while the inert doublet η and RHNs N carry Z2 charge −. The spontaneous breaking of U(1) B-L generates RHN masses Mi = Yi N vφ/√2, and the Majoron field is defined as θ ≡ J/vφ. The scalar potential includes the λ5 term, which is essential for neutrino mass generation at one loop.

The neutrino mass matrix is generated radiatively, with the mass formula given by (Mν)αβ = (vΦ 2/32π 2) Σ i (Y ν αi Y ν βi ξ i / M i), where ξ i encodes the loop suppression and depends on λ5. The paper notes: the smallness of neutrino masses is naturally associated with the smallness of the symmetry-breaking parameter λ5.

For inert doublet DM, the paper focuses on the CP-odd scalar ηI as the DM candidate, requiring λ5 > 0. The viable parameter region for ηI as dominant DM is mηI ≳ 550 GeV, with 10-6 ≲ λ5 ≲ 0.2, constrained by relic density, direct detection (LZ-2024), LEP, electroweak precision, and vacuum stability. The paper states: in this setup the correct DM relic abundance (assuming ηI constitutes 100% of the observed DM abundance) can be obtained for 550 ≲ mηI/GeV ≲ 1000, 10-6 ≲ λ5 ≲ 0.2.

For conventional thermal leptogenesis, the paper shows that the decay parameter K1 is always in the strong washout regime (K1 > 10 4 for M1 = 1 TeV), leading to a lower bound M1 ≳ 10 11 GeV for successful leptogenesis. This motivates the spontaneous leptogenesis mechanism, which thrives in the strong washout regime.

The spontaneous leptogenesis mechanism works as follows: the Majoron background θ̇ generates an effective chemical potential for B-L via the derivative interaction L ⊃ -(1/2)θ̇ n B-L. The B-L-violating decays and inverse decays N1 ↔ lLα η remain in thermal equilibrium, biasing the plasma towards a nonzero B-L asymmetry. The final baryon asymmetry is given by YB = (cB/6) Yθ (M1/(vφ zdec)) squared, where zdec corresponds to the inverse decay decoupling temperature, or by a similar expression with zsp if sphaleron decoupling occurs first.

The paper presents parameter space plots showing successful leptogenesis for a wide range of M1 and vφ. For example, with λ5 = 10-2 and λ5 = 10-4, the required Majoron yield Yθ is shown as a function of M1, with the condition that the Majoron kinetic energy remains subdominant to radiation at freeze-out (to maintain radiation domination). The paper notes: successful low-scale leptogenesis is most easily realized for moderately small symmetry breaking scales.

The role of λ5 in spectator processes is analyzed in detail. For λ5 = 10-2, the λ5 interaction remains in thermal equilibrium, modifying the spectator coefficient cB relative to the type-I seesaw case. For λ5 = 10-4, the interaction becomes efficient only below Td ≃ 5 × 10 6 GeV, so for inverse decay decoupling above this temperature, µη must be treated as independent (with µη ≃ 0). The paper derives the conversion factors cB for different temperature regimes in the Appendix.

The paper also examines Majoron DM from kinetic misalignment. The kinetic misalignment condition is Yθ > Ycr, where Ycr is given by Eq. (39). The Majoron relic abundance is controlled by Yθ, and the requirement that Majoron DM does not overclose the Universe gives Yθ ≤ Yθ DM. The paper shows allowed regions in the Yθ vs mJ plane for vφ = 10 8 and 10 10 GeV, with constraints from Majoron decay to neutrinos (requiring τJ > 250 Gyr) and overproduction.

The Majoron mass is constrained by cosmological stability: for mJ > 2mνi, the Majoron can decay to neutrinos, and the decay width is Γ(J → νiνi) = (mJ/16π)(mνi/vφ) squared √(1 - 4mνi 2/mJ 2). For TeV-scale RHNs, the most stringent constraint is mJ ≲ 0.0182 eV for vφ = 10 4 GeV. The paper notes: with mJ ≲ 0.017 eV, the Majoron becomes kinematically forbidden to decay to neutrinos, making it cosmologically stable against neutrino pair decays.

The paper also estimates the dark radiation contribution from thermal Majoron quanta, finding ∆Neff ≃ 0.025, which is below current bounds but within the reach of future CMB probes.

In conclusion, the paper states: "Our results therefore, show that the dynamical scotogenic model provides an economical realization of spontaneous leptogenesis in which the origin of neutrino masses, IHD DM, and the baryon asymmetry are linked to the same symmetry breaking structure. The possibility of successful leptogenesis with TeV-scale hierarchical RHNs makes this framework a unique and testable alternative to high-scale thermal leptogenesis, with correlated probes from DD experiments, inert scalar and missing energy searches at colliders, and future measurements of dark radiation."

Improvements to AI Systems Based on This Paper:

1. Low-Scale Baryogenesis Simulation Engine

• Capability: An AI system can now model and predict baryon asymmetry generation at TeV-scale RHN masses (down to 600 GeV), bypassing the conventional 10 11 GeV lower bound.

• Specific use: Automatically scan parameter space (M1, vφ, λ5, Yθ) to identify viable regions for successful leptogenesis in strong washout regimes, reducing manual computation time by orders of magnitude.

2. Unified Multi-Physics Solver for Cosmological Observables

• Capability: Simultaneously solve for neutrino masses (radiative loop), inert scalar DM relic density, Majoron DM abundance, and baryon asymmetry within one framework.

• Specific use: Generate correlated predictions for direct detection cross-sections, collider missing energy signatures, and ∆Neff (dark radiation) from a single input parameter set, enabling fast model discrimination against future LZ, HL-LHC, and CMB-S4 data.

3. Spectator-Coupling-Aware Chemical Potential Calculator

• Capability: Automatically compute the conversion factor cB (baryon-to-B-L asymmetry) under temperature-dependent spectator processes, including the λ5-mediated interactions that modify equilibrium conditions.

• Specific use: For any given λ5 and decoupling temperature, the AI can instantly determine whether µη must be treated as independent or equilibrated, avoiding incorrect asymmetry predictions in low-scale leptogenesis models.

4. Majoron Dark Matter Stability and Relic Forecaster

• Capability: Predict Majoron mass ranges (e.g., mJ ≲ 0.018 eV for vφ = 10 4 GeV) that ensure cosmological stability against neutrino decays, while simultaneously checking kinetic misalignment relic abundance and overclosure constraints.

• Specific use: Automatically flag parameter regions where Majoron DM is viable and stable, and output expected signals for future MeV-scale DM detectors or CMB spectral distortion experiments.

5. Automated λ5-Role Identifier for DM Asymmetry Erasure

• Capability: Determine whether the λ5 interaction is in equilibrium at a given temperature and quantify its impact on inert scalar DM asymmetry survival.

• Specific use: For a proposed model, the AI can instantly classify whether the DM candidate (ηI) will retain a primordial asymmetry or be erased, guiding relic density calculations without manual Boltzmann equation solving.

6. Cross-Experiment Correlated Probe Generator

• Capability: Generate a single testability map linking low-scale leptogenesis parameters to observable signatures across direct detection (LZ-2024), collider searches (inert scalar pair production, missing energy), and future dark radiation measurements (∆Neff 0.025).

• Specific use: Given a hypothetical experimental null result in one channel, the AI can update posterior probabilities for the model and predict which other channels become most promising, enabling adaptive experimental strategy.

7. Temperature-Regime-Aware Sphaleron Decoupling Handler

• Capability: Automatically switch between inverse-decay decoupling (zdec) and sphaleron decoupling (zsp) regimes in the baryon asymmetry formula, based on the model’s RHN mass and vφ.

• Specific use: For a new model input, the AI instantly identifies which decoupling dominates and computes the correct final YB, avoiding errors from using a single formula across all parameter space.

8. Radiative Neutrino Mass Loop Integrator with λ5 Feedback

• Capability: Precisely compute the loop suppression factor ξ i (dependent on λ5) and its back-reaction on the neutrino mass matrix, ensuring consistency between the symmetry-breaking parameter and observed neutrino oscillation data.

• Specific use: The AI can invert the problem—given neutrino mass splittings and mixing angles, it can output allowed λ5 ranges and corresponding RHN Yukawa couplings, directly feeding into leptogenesis and DM calculations.

9. Multicomponent Dark Sector Relic Allocator

• Capability: Automatically partition the total DM relic density between inert scalar (ηI) and Majoron (J) based on kinetic misalignment conditions, including constraints from direct detection and Majoron decay lifetime.

• Specific use: For a given vφ and Yθ, the AI outputs the fractional DM abundance of each component and flags regions where both can coexist without violating observational bounds—enabling rapid exploration of mixed DM scenarios.

10. Automated Washout Regime Classifier

• Capability: Instantly compute the decay parameter K1 for any RHN mass and Yukawa coupling, and classify the regime (strong/weak washout) to determine whether spontaneous leptogenesis or conventional thermal leptogenesis applies.

• Specific use: The AI can pre-screen candidate models and reject those requiring M1 > 10 11 GeV, focusing computational resources on testable low-scale scenarios—accelerating model discovery by filtering out high-scale dead ends.

We propose a low-scale spontaneous leptogenesis scenario within the dynamical minimal scotogenic model for accommodating neutrino masses and inert scalar dark matter simultaneously. Thus, we dub the mechanism Spontaneous Scoto-leptogenesis. In this setup, a rolling Majoron arising from the global U(1) B-L symmetry breaking induces an effective chemical potential for the B-L charge in the presence of B-L violating interactions that allow for the efficient decays and inverse decays of right handed neutrinos (RHN), so it gives rise to the observed baryon asymmetry of the Universe through the electroweak sphaleron conversion. The mechanism becomes effective in the strong washout regime and successfully lowers the viable mass scale of the lightest RHN to the range of TeV scales, thereby making the thermal scotogenic leptogenesis with two hierarchical RHNs accessible to direct tests. We identify the roles of the lambda 5 coupling for spontaneous leptogenesis and inert scalar dark matter through the efficient erasure of the inert scalar asymmetry. We also explore the regime for Majoron dark matter from the kinetic misalignment, showing that a multicomponent dark sector comprising the inert scalar and the Majoron can be realized in the model. The resulting framework provides a unified origin for low-scale baryogenesis, neutrino masses, and multicomponent dark sector, so it can be tested by complementary experimental probes through direct detection experiments, collider searches for inert scalars, and future detection of Majoron dark matter or dark radiation.