How to find neutral leptons of the nuMSM?

TL;DR

The paper assesses the neutrino Minimal Standard Model (νMSM), which adds three light singlet fermions to the Standard Model to address neutrino masses, dark matter, and baryon asymmetry. It derives the Lagrangian, parameter relations, and flavor couplings constrained by neutrino data and cosmology, and establishes both upper and lower bounds on the heavy-lepton mixing $U^2$ (including a strong BBN-derived lower bound for sub-GeV masses). It then analyzes production and decay channels of heavy neutral leptons across the 0.01–5 GeV range, highlighting the dominant meson sources (kaons, D_s, B) and the resulting experimental signatures, including missing-energy kaon decays and displaced decays in fixed-target and near-detector setups. The work emphasizes that probing the νMSM parameter space below the kaon threshold may be achievable with reanalysis of existing kaon data and dedicated near-detector experiments, while heavier regions require high-intensity proton-beam facilities or specialized beam-dump experiments. Overall, the paper outlines practical pathways and benchmarks for testing νMSM predictions with current and near-future experimental infrastructure, linking cosmological constraints to concrete search strategies.

Abstract

An extension of the Standard Model by three singlet fermions with masses smaller than the electroweak scale allows to explain simultaneously neutrino oscillations, dark matter and baryon asymmetry of the Universe. We discuss the properties of neutral leptons in this model and the ways they can be searched for in particle physics experiments. We establish, in particular, a lower and an upper bound on the strength of interaction of neutral leptons coming from cosmological considerations and from the data on neutrino oscillations. We analyse the production of neutral leptons in the decays of different mesons and in $pp$ collisions. We study in detail decays of neutral leptons and establish a lower bound on their mass coming from existing experimental data and Big Bang Nucleosynthesis. We argue that the search for a specific missing energy signal in kaon decays would allow to strengthen considerably the bounds on neutral fermion couplings and to find or definitely exclude them below the kaon threshold. To enter into cosmologically interesting parameter range for masses above kaon mass the dedicated searches similar to CERN PS191 experiment would be needed with the use of intensive proton beams. We argue that the use of CNGS, NuMI, T2K or NuTeV beams could allow to search for singlet leptons below charm in a large portion of the parameter space of the nuMSM. The search of singlet fermions in the mass interval 2-5 GeV would require a considerable increase of the intensity of proton accelerators or the detailed analysis of kinematics of more than 10^{10} B-meson decays.

Figures (17)

• Figure 1: Limits on $|U_e|^2$, $|U_e||U_\mu|$ and $|U_\mu|^2$ for three benchmark models (I-III from left to right) from BBN (lower bound) and from direct searches in the CERN PS191 experiment (upper bound). Blank regions are phenomenologically allowed.
• Figure 2: Branching ratios of neutrino two-body decays $N_I\to XY$ as functions of neutrino mass $M_N$ for models with the same hierarchy in mixing as in models: a) I, b) II, c) III; different lines correspond to different modes: $\pi\nu$ (solid black), $\pi e$ (short-dashed black), $\pi\mu$ (long-dashed black), $Ke$ (solid light gray), $\eta\nu$ (solid dark gray), $\eta'\nu$ (short-dashed dark gray), $K\mu$ (dashed light gray), $\rho \nu$ (solid gray), $\rho e$ (short-dashed gray), $\rho\mu$ (long-dashed gray).
• Figure 3: Branching ratios of neutrino three-body decays $N_I\to ABC$ as functions of neutrino mass $M_N$ for models with the same hierarchy in mixing as in models: a) I, b) II, c) III; different lines correspond to different modes: $\bar{\nu} \nu\nu$ (sum over all invisible modes, solid black), $\nu e^+e^-$ (solid gray), $\nu e\mu$ (sum over two modes, long-dashed gray), $\nu \mu^+\mu^-$ (short-dashed gray).
• Figure 4: a) Upper (solid lines) and lower limits (dashed lines) on neutrino lifetime in models I (black), II (dark gray) and III (light gray); a horizontal thick solid black line indicates the upper limit from BBN, $\tau_N<0.1$ c, suggested in Ref.Dolgov:2000jw, thin solid lines are limits from eq. \ref{['lower']}, thick dashed lines refer to eq. \ref{['upper']}, thin dashed lines correspond to limits from direct searches for sterile neutrinos discussed in Section \ref{['Sec:exp-limits']}; charge-conjugated modes are accounted. b) Lower (solid lines) and upper limits (dashed lines) on overall mixing $U^2$ in models I (black), II (dark gray) and III (light gray). Thin solid lines and thick dashed lines depict limits from eqs. \ref{['lower']} and \ref{['upper']}, respectively. Thick solid lines indicate lower limits from order-of-magnitude BBN bound on neutrino lifetime, $\tau_N<0.1$ c for $M_N>140$ MeV, thin dashed lines refer to limits from direct searches for sterile neutrinos discussed in Section \ref{['Sec:exp-limits']}.
• Figure 5: Branching ratios of decays $K\to e N_I$ (solid lines) and $K\to \mu N_I$ (dashed lines) as functions of heavy neutrino mass $M_N$ in models: a) I, b) II, c) III. In a phenomenologically viable model and heavy neutrino mass within $M_\pi\lesssim M_N\lesssim M_K$, the branching ratios are confined between corresponding thin and thick lines which show upper and lower limits on $U^2$ from Fig. \ref{['Nu-lifetime']}b, respectively.