Big Bang Nucleosynthesis and the Neutrino-Extended Standard Model Effective Field Theory

TL;DR

The paper investigates GeV-scale heavy neutral leptons within the neutrino-extended SM EFT ($\nu$SMEFT) and shows that cosmological BBN considerations impose robust upper bounds on the new-physics scale $\Lambda$ for $M_4\gtrsim100\,\text{MeV}$, complementing collider and fixed-target constraints. By mapping the high-energy EFT to a low-energy $\nu$LEFT theory and analyzing HNL production and decay through Boltzmann evolution, it connects the HNL thermal history to BBN outcomes, including both stable and decaying scenarios. The work demonstrates that BBN bounds, together with neutrinoless double beta decay and displaced-vertex searches, carve out well-defined target regions in the $\nu$SMEFT parameter space and highlights the potential of cosmology to constrain EFT operators that couple HNLs to SM fields. Through explicit examples and a broad scan of LR and leptoquark-inspired scenarios, the authors identify where future DV experiments (ANUBIS, DUNE, SHiP) and next-generation $0\nu\beta\beta$ experiments can most effectively probe the νSMEFT operators governing HNLs. Overall, the study provides a systematic cosmological complement to laboratory probes, guiding experimental efforts to test GeV-scale HNLs within a general EFT framework.

Abstract

We study the impact of light GeV-scale heavy neutral leptons (HNLs) on Big Bang nucleosynthesis (BBN) in the neutrino-extended Standard Model Effective Field Theory ($ν$SMEFT). We show that, based on very general considerations, BBN constraints complement laboratory searches at colliders, beam dumps, and neutrinoless double beta decay, by providing an upper bound on the cut-off scale of the effective field theory for HNL masses above $\sim$100 MeV. We identify target regions for future laboratory probes of the $ν$SMEFT parameter space that is bounded from above and below.

Figures (3)

• Figure 1: The factor $\alpha_i(M_4)$ as defined in Eq. \ref{['eq:m4bound']} in an EFT scenario where $C_{du\nu \ell,111}=1/\Lambda^2$. The total decay rate $\Gamma_N$ is calculated assuming hadronic substructure (the quark-current approximation) for $\alpha^\text{Hadr}_{du\nu \ell,111}$$(\alpha^\text{QC}_{du\nu \ell,111})$. In this scenario, the mass threshold for the quark-current approximation is $M_4\gtrsim1.2\,$GeV. The HNLs decouple non-relativistically for masses highlighted in blue.
• Figure 2: The left panel shows freeze-out HNL abundances $Y_N^f$ obtained by solving the Boltzmann equation in Eq. \ref{['eq:sterile_production']} neglecting HNL decays, while the right panel shows the HNL yield $Y_N$ at the onset of BBN including decays. The white dashed line shows the conservative relativistic freeze-out condition from Eq. \ref{['eq:TfLambda']}. The simplified BBN bound ($\tau_N > 0.02\,\mathrm{s}$) is shown by the violet dot-dashed line, and is fully compatible with $Y_N^f > 10^{-3}$ in the region of parameter space indicated by the solid red line. For smaller HNL masses, we can see that the dot-dashed violet crosses the red line around $M_\pi$, where the HNLs become stable. The computation with the HNL decays included (right) shows almost perfect agreement with the simplified violet dot-dashed BBN bound.
• Figure 3: For $C_{du\nu \ell,111}=1/\Lambda^2$ scenario with a fixed $\Lambda=50$ TeV, the left panel shows the HNL lifetime (blue) and the BBN lifetime bound determined by Eq. \ref{['eq:BBNlifetimelim']} (red). The right panel shows the exclusion limits on the NP scale imposed by BBN lifetime constraints (red) and current-generation constraints on the ${}^{136}\text{Xe}$$0\nu\beta\beta$ half-life (cyan), along with projected next-generation $0\nu\beta\beta$ constraints (blue).