Heavy neutral leptons beyond the BBN bound: probing the lepton asymmetry of the Universe

This paper, Heavy neutral leptons beyond the BBN bound: probing the lepton asymmetry of the Universe by Kensuke Akita, Maksym Ovchynnikov, and Vsevolod Syvolap, proposes a mechanism by which heavy neutral leptons (HNLs) can evade the Big Bang Nucleosynthesis (BBN) bound that otherwise excludes hadronically decaying particles with lifetimes τ ≳ 0.02 s.

The Problem: "Hadronically decaying particles with lifetimes τ ≳ 0.02 s are excluded by Big Bang Nucleosynthesis almost independently of their abundance: the mesons from their decays convert protons into neutrons faster than the reverse, and helium is overproduced. For HNLs, this blankets the couplings the upcoming accelerator searches can reach. The standard BBN bound arises because HNLs with mN > mlα + mπ decay as N → π+ lα−, and the injected charged pions interconvert nucleons through strong reactions such as π− + p → n + π0/γ, whose cross sections exceed the weak p ↔ n rates at MeV temperatures by sixteen orders of magnitude. In the minimal scenario, decays of HNLs inject equal numbers of π+ and π−, and this drives the neutron fraction towards the isospin-symmetric value n/p ≃ 1, overproducing helium and deuterium. The resulting bound is τN ≲ 0.02 s and is nearly universal for any hadronically decaying relic."

The Proposed Mechanism: The authors "identify and test, to our knowledge, the first mechanism by which a mixing-produced population of hadronically decaying particles can leave the BBN observables inside their observational windows. It operates in the presence of large lepton flavor asymmetries. For a Dirac HNL, GeV-mass N injects π+ and N̄ injects π−, since each charged pion is emitted together with the charged lepton carrying the parent's lepton number. An asymmetry LN ≡ (nN − nN̄)/s makes the decays inject unequal numbers of π+ and π−, and can return the neutron abundance to its standard value. For the CMB, the relaxation comes from the cancellation between the two impacts on Neff: the asymmetries raise it, while the HNL decays deplete it."

The Physics: While mesons are present, the neutron fraction Xn = nn/(nn + np) tracks the quasi-static equilibrium of the strong p ↔ n reactions. For a Dirac population with number ratio r ≡ nN/nN̄, the equilibrium reduces to Xn ≃ Cπ/(Cπ + r), where Cπ = ⟨σv⟩πp→n/⟨σv⟩πn→p = O(1), exceeding unity owing to the Coulomb attraction in the π−p channel. Choosing rreq = Cπ(1 − XnSBBN)/XnSBBN ≃ 4–10 pins the neutron fraction at the value the standard evolution reaches when the mesons die out, and the BBN bounds are relaxed.

Parameter Space Opened: The mechanism opens the parameter space with ml + mπ ≲ mN ≲ 1 GeV and τN ≲ 1 s, including a substantial region within the reach of SHiP. The mechanism may operate kinematically for mlα + mπ ≲ mN ≲ 1.5 GeV: at larger masses, N itself emits both π+ and π−, as well as the charge-blind KL, eroding the achievable imbalance below 1/rreq.

Computational Framework: The authors use a coupled pipeline of three stages: (1) momentum-resolved Boltzmann evolution of HNL production down to T = 20 MeV with plasma charge redistribution; (2) flavor dynamics sourced by asymmetric decays using quantum kinetic equations; (3) evolution through neutrino decoupling and BBN with νDSMC, extended by the dynamics of metastable decay products of HNLs. They note this is the first calculation to follow a large lepton flavor asymmetry through the flavor dynamics and the momentum-resolved neutrino evolution in the presence of a relic that decays into non-thermal neutrinos and mesons.

Observational Constraints: The authors adopt ∆Neff ≤ 0.05 as the band where HNLs leave no CMB imprint, use YP = 0.2458 ± 0.0013 for helium, and adopt the higher deuterium prediction (2.51 ± 0.07) which agrees with the observed 105 × D/H = 2.55 ± 0.03. They use a two-sigma deuterium window, ∆(D/H)/(D/H) ≤ 0.031.

Four Regions of Parameter Space:

• Region 1 (invisible): YP, D/H, and Neff all sit inside the windows above and the HNLs leave no imprint on BBN or the CMB.

• Region 2 (Neff deficit): The decays deplete Neff while the compensating asymmetries raise it; the residual is set by how completely the two cancel. They target −0.28 ≤ ∆Neff ≤ −0.05, the direction of the uncompensated HNL effect itself.

• Region 3 (CνB enhancement): the total neutrino number density, the leading factor in that rate, can be enhanced by more than 30% relative to the standard ν sea. This persists even where ∆Neff is tiny.

• Region 4 (GW target): Large compensated flavor asymmetries drive the quark chemical potentials at the QCD epoch... the trajectory of the quark chemical potentials can therefore cross the critical surface... making the transition first order, which would source a stochastic gravitational wave background.

Key Results: The mechanism works for HNLs mixing with the muon flavor, with the parameter space shown in Fig. 1. Two benchmark solutions are given: (0.5 GeV, 0.05 s) with qN = +0.35 and ξ20 = (+0.00, −0.05, +1.83), probing SHiP and CνB; and (0.7 GeV, 0.022 s) with qN = +0.20 and ξ20 = (−2.98, +0.48, +1.95), probing SHiP, CMB, and GW.

Implications: "An HNL discovery at (mN, τN) inside the domains of Fig. 1 would constrain the primordial asymmetries to the one-parameter family identified above, along which only the sharing of the asymmetry between the electron and tau flavors is left free. The scenario requires lepton number must be conserved to an excellent approximation (δm ≲ ħ/τN ≃ 10−15 eV), and if the light neutrinos acquire their masses from the same lepton-number-conserving sector, they are Dirac."

Model Example: The scenario can be realized via Affleck-Dine leptoflavorgenesis for generating compensated flavor asymmetries, with a Dirac HNL embeds naturally under an exactly conserved global lepton number, which forbids Majorana masses.

Conclusions: "We have shown that the meson-driven BBN bound can be lifted for hadronically decaying relics that inherit part of the lepton flavor asymmetries, without modifying their laboratory decay rates. We thereby propose a new target for accelerator searches: sub-GeV HNLs with lifetimes naively excluded in standard cosmology. The correlated signatures turn a detection into a measurement of the primordial flavor asymmetries."

Improvement 1: Physics-constrained parameter-space inference for relic decays

The AI system can now incorporate the mechanism’s core condition—lepton flavor asymmetries (ξ e, ξ μ, ξ τ) and HNL charge asymmetry q N—as free parameters when fitting BBN/CMB observables. Instead of assuming symmetric decays, it can solve for the required asymmetry ratio r req = C π(1 − X n SBBN)/X n SBBN (with C π ≈ 4–10) to predict whether a given (m N, τ N) point is allowed. This enables automated scanning of the newly opened parameter space (m N ∈ [m l + m π, 1 GeV], τ N ≲ 1 s) and identification of viable regions for SHiP-like searches.

Improvement 2: Multi-stage coupled evolution solver

The AI can now run a three-stage pipeline—(1) momentum-resolved Boltzmann for HNL production with plasma charge redistribution, (2) quantum kinetic equations for flavor dynamics under asymmetric decays, (3) νDSMC evolution through neutrino decoupling and BBN with metastable decay products—to self-consistently compute X n, Y P, D/H, and N eff. This replaces simplified single-zone models, allowing the AI to predict non-trivial correlations (e.g., N eff depletion vs. asymmetry compensation) that standard codes miss.

Improvement 3: Observable-window classification and target prioritization

The AI can classify any (m N, τ N, q N, ξ α) point into four regions: (1) invisible (all observables within bounds), (2) N eff deficit (−0.28 ≤ ΔN eff ≤ −0.05), (3) CνB enhancement (>30% neutrino density increase), (4) GW source (first-order QCD transition from quark chemical potentials). This enables automated ranking of experimental targets—e.g., flagging points where SHiP detection would simultaneously imply a measurable CνB excess or a stochastic GW background, guiding multi-messenger follow-up.

Improvement 4: Lepton-number-conservation consistency checks

The AI can now enforce the constraint δm ≲ ħ/τ N (≈10−15 eV for τ N 0.02–1 s) and verify that the scenario implies Dirac neutrinos if masses arise from the same sector. It can also test whether a given asymmetry configuration is realizable via Affleck-Dine leptoflavorgenesis, rejecting parameter sets that violate exact global lepton number conservation.

Improved AI system capabilities:

• Predictive scanning: Given a proposed HNL mass and lifetime, the AI outputs the full allowed range of primordial flavor asymmetries and the resulting BBN/CMB signatures, including whether the point is observable by SHiP, CMB-S4, or LISA.

• Inverse problem solving: From a hypothetical HNL detection (m N, τ N) and measured N eff or D/H deviation, the AI reconstructs the one-parameter family of lepton asymmetries (fixing the electron–tau sharing degeneracy) and predicts the associated CνB enhancement or GW signal.

• Model discrimination: The AI can distinguish this asymmetry-driven relaxation from alternative BBN-evasion mechanisms (e.g., entropy dilution, modified expansion rate) by checking for the characteristic signature of unequal π+/π− injection and the required r req value.

• Experimental design: The AI can optimize future accelerator beam-dump experiments (e.g., SHiP, FASERν) by identifying the (m N, τ N) sub-regions where the BBN bound is relaxed and where correlated cosmological signatures (N eff dip, CνB excess, GW) are maximally detectable, thus informing exposure time and detector sensitivity requirements.

Hadronically decaying particles with lifetimes tau 0.02, s are excluded by Big Bang Nucleosynthesis almost independently of their abundance: the mesons from their decays convert protons into neutrons faster than the reverse, and helium is overproduced. For heavy neutral leptons (HNLs), this blankets the couplings the upcoming accelerator searches can reach. We propose a scenario with large lepton flavor asymmetries in which HNLs evade it. A Dirac HNL decays into pi+ and its antiparticle into pi-, so an asymmetry between the two populations injects an excess of pi+, which converts the neutrons back to their standard abundance, while a cancellation between the asymmetries and the HNL decays keeps the shift in N eff small. This opens the parameter space with m l+m pi m N 1, GeV and tau N 1, s, including a substantial region within the reach of SHiP. A discovery there, combined with the BBN and CMB observables, would fix the primordial flavor asymmetries up to one remaining direction. The relic neutrino background and a possibly first-order cosmic QCD transition, a source of gravitational waves, may probe that direction, and with it the lepton asymmetry of the Universe.