Search for heavy neutral leptons in $π^+$ decays to positrons

A search for heavy neutral lepton ($N$) production in $π^+\to e^+ N$ in-flight decays using data collected by the NA62 experiment at CERN in 2017-2024 is reported. Upper limits for the extended neutrino mixing matrix element $|U_{e4}|^2$ are established at the level of $10^{-8}$ for heavy neutral leptons with mass in the range 95-126 $MeV/c^2$ and lifetime exceeding 50 ns.

💡 Research Summary

The NA62 collaboration presents a search for heavy neutral leptons (HNLs), denoted N, produced in the two‑body decay π⁺ → e⁺ N using data collected between 2017 and 2024. In the νMSM framework, three right‑handed neutrinos are added to the Standard Model, providing a mechanism for neutrino masses, dark matter, and the baryon asymmetry. If the HNL mass lies below the kinematic limit m_N < m_{π⁺} – m_e ≈ 139 MeV/c², it can be emitted in pion decay with a branching fraction

B(π⁺ → e⁺ N) = B(π⁺ → e⁺ ν_e) · ρ(m_N) · |Uₑ₄|²,

where ρ(m_N) is a phase‑space factor that equals one for a massless HNL and vanishes at the endpoint. The goal of the analysis is to set limits on the mixing element |Uₑ₄|² in the mass interval 95–126 MeV/c², assuming the HNL lifetime exceeds 50 ns so that it does not decay inside the detector.

The NA62 beamline delivers a 75 GeV/c secondary beam composed of ≈70 % π⁺, 23 % protons and 6 % K⁺, generated by 400 GeV/c SPS protons on a beryllium target. The detector suite includes the GTK silicon‑pixel beam tracker, the STRAW vacuum spectrometer, a Ring‑Imaging Cherenkov (RICH) detector, a liquid‑krypton electromagnetic calorimeter (LKr), and a set of photon and muon vetoes (LAV, IRC, SAC, MUV). The trigger system consists of a hardware level (L0) requiring RICH multiplicity, CHOD activity and LKr energy, and a software level (L1) imposing a KTAG coincidence, a positively‑charged STRAW track with p < 50 GeV/c, and vetoes on large‑angle photons.

Signal candidates are required to have a single positively‑charged track reconstructed in STRAW with momentum 5–30 GeV/c, identified as an electron by E/p ≈ 1 and RICH pattern, and matched in time and space to a GTK beam particle (|Δt| < 0.5 ns, closest‑approach distance < 3 mm). The decay vertex, defined by the intersection of the GTK and STRAW tracks, must lie inside the 75 m fiducial volume and at least 5 m downstream of the beam entrance to suppress upstream decays. Additional vetoes reject extra tracks, photon activity in LAV/IRC/SAC, and muon signals in MUV.

The analysis uses the missing‑mass squared variable m²_miss(π) = (P_π – P_e)², where P_π is the four‑momentum of the beam particle measured by GTK and P_e is the positron four‑momentum from STRAW and LKr. Standard Model π⁺ → e⁺ ν_e decays produce a narrow peak at m² ≈ 0 with a resolution σ_m² ≈ 3.3 × 10⁻⁴ GeV²/c⁴. An HNL would appear as an additional narrow peak at m² = m_N². Backgrounds arise mainly from K⁺ → μ⁺ ν_μ and π⁺ → μ⁺ ν_μ decays followed by muon decay in flight, as well as from accidental activity. These are suppressed by the photon and muon vetoes and by the stringent kinematic cuts; the residual background shape is smooth across the search region.

Normalization of the π⁺ and K⁺ decay rates is performed using the abundant SM π⁺ → e⁺ ν_e and K⁺ → e⁺ ν_e samples in defined missing‑mass windows. The numbers of π⁺ and K⁺ decays in the fiducial volume (N_π ≈ 6.5 × 10¹², N_K ≈ 1.9 × 10¹³) are derived from the observed events, corrected for acceptance (evaluated with Geant4‑based Monte Carlo) and the known branching fractions.

The HNL search scans 63 mass hypotheses uniformly spaced by 0.75 σ_m (σ_m being the local missing‑mass resolution). For each hypothesis a signal window of ±1.5 σ_m around m_N² is defined, and sidebands from 1.5 σ_m to 9 σ_m are used to model the background with a third‑order polynomial. Systematic uncertainties on the background estimate are obtained by varying the polynomial order (3↔4) and the sideband definitions (8.25 σ_m ↔ 9.75 σ_m). The signal acceptance A_N, obtained from simulation, varies from ≈0.5 % to 0.8 % across the mass range. The single‑event sensitivity is B_SES = 1/(N_π · A_N), leading to a mixing‑element sensitivity |Uₑ₄|²_SES = B_SES · B(π⁺ → e⁺ ν_e) · ρ(m_N).

No excess over the smooth background expectation is observed for any mass hypothesis. Using the Feldman‑Cousins approach, 90 % confidence‑level upper limits on the number of signal events are translated into limits on |Uₑ₄|². The resulting limits range from 5 × 10⁻⁹ to 1.5 × 10⁻⁸, depending on the HNL mass, representing an improvement of one to two orders of magnitude over previous π⁺‑decay searches (PIENU) and complementing the NA62 K⁺ → e⁺ N results which probe lower mixing values at higher masses.

In summary, the NA62 experiment has performed the most sensitive search to date for HNLs produced in π⁺ → e⁺ N decays in the mass window 95–126 MeV/c², setting stringent constraints on the electron‑flavour mixing parameter |Uₑ₄|² at the 10⁻⁸ level for lifetimes longer than 50 ns. These results significantly narrow the viable parameter space of low‑mass HNLs in the νMSM and demonstrate the power of high‑intensity pion beams combined with precise missing‑mass techniques. Future data taking with higher beam intensity and upgraded detectors could push the sensitivity down to the 10⁻⁹ regime, further testing the heavy‑neutral‑lepton hypothesis.