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

Abstract

Hadronically decaying particles with lifetimes $\tau\gtrsim0.02\,{\rm s}$ 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 $N_{\rm eff}$ small. This opens the parameter space with $m_l+m_\pi\lesssim m_N\lesssim1\,{\rm GeV}$ and $\tau_N\lesssim1\,{\rm s}$, 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.