Exploring Invisible New Physics with Exotic Pion Decays

TL;DR

This work evaluates how stopped-pion experiments can discover or constrain light invisible dark-sector particles produced in exotic pion decays. It analyzes two- and three-body decay channels, recasts PIENU limits, and provides detailed projections for the upcoming PIONEER experiment, showing at least an order-of-magnitude improvement in exotic-pion branching-ratio bounds. The authors develop a unified framework for sterile-neutrino searches and for three-body decays into scalars, ALPs, and vectors, including realistic detector effects and background considerations. By comparing with lepton g-2, mono-photon, beam-dump, and kaon-decay constraints, they identify weak-violating ALPs as a particularly well-motivated benchmark and demonstrate PIONEER’s complementary role in light dark-sector exploration.

Abstract

We study the sensitivity of past and future stopped-pion experiments to light, invisible dark sector particles produced in exotic pion decays. We consider two-body decays involving sterile neutrinos, $π^+ \to \ell^+ N$, as well as three-body decays $π^+ \to \ell^+ ν_\ell X$, with $X$ an invisible scalar, axion-like particle, or dark vector. We recast existing limits from the PIENU experiment and project the reach of the planned PIONEER experiment using detailed simulations based on the current detector design. We find that PIONEER can improve bounds on exotic pion branching ratios by at least one order of magnitude below current limits. We compare the projected sensitivities with complementary constraints from lepton anomalous magnetic moments, mono-photon searches, and beam-dump experiments, identifying weak-violating axion-like particles as a particularly well-motivated benchmark. Our results establish PIONEER as a powerful and complementary probe of light, invisible dark sectors.

Figures (15)

• Figure 1: Constraints from pion decays $\pi^+ \to e^+ N$ on the sterile neutrino mixing angle $|U_{e N}|^2$ at 90% C.L. as a function of the sterile neutrino mass $m_N$. The PIENU result from PIENU:2017wbj is shown by the dotted red line. Our reproduction of the PIENU bound is shown in solid red. The corresponding limit from NA62 NA62:2025csa is shown in gray. The bound from the $R_\pi$ measurement is shown in dashed red. The red and gray shaded regions are excluded. The solid blue and the dashed blue curves correspond to our sensitivity estimates of a PIONEER search for sterile neutrinos and the PIONEER $R_\pi$ measurement, respectively. The yellow shaded region indicates a see-saw target (see text for more details). This region can be reached by PIONEER for $64~{\rm{MeV}}\lesssim m_N\lesssim 130$ MeV.
• Figure 2: Constraints on the sterile neutrino mixing angle $|U_{\mu N}|^2$ at 90% C.L. as a function of the sterile neutrino mass $m_N$. The PIENU result from PIENU:2019usb is shown by the dotted red lines. Our reproduction of the PIENU bound is shown in solid red. The bound from the $R_\pi$ measurement is shown in dashed red. The shaded regions are excluded. The solid blue and the dashed blue curves correspond to our sensitivity estimates of a PIONEER search for sterile neutrinos and the PIONEER $R_\pi$ measurement, respectively. The see-saw target (indicated with the yellow band) is out of the PIONEER reach.
• Figure 3: The expected positron energy spectrum at phase I of PIONEER after background suppression cuts. Shown in blue are $0.5 \times 10^8$$\pi^+ \to e^+ \nu_e (\gamma)$ events and in red dashed an $8.8\%$ contamination from muon decays in flight, $\mu_{\rm{DIF}}$.
• Figure 4: Sensitivity to the sterile neutrino mixing angle $|U_{e N}|^2$ at 90% C.L. as a function of the sterile neutrino mass $m_N$ from a bump search at PIONEER. The solid line takes into account statistical uncertainties on the event numbers and allows for a floating normalization of background keeping the background shape fixed. The dashed, dot-dashed, and dotted lines include in addition uncorrelated systematic uncertainties of 1%/3%/5% in each positron energy bin.
• Figure 5: Representative examples of normalized signal shapes of the $\pi^+ \to e^+ \nu_e X$ decay as a function of the positron energy. Top: scalar and ALP models; bottom: various vector models. For a mass of $m_X = 120$ MeV, the spectra of the vector models with $g_V$ coupling and $g_T$ coupling are almost indistinguishable. The spectra of the vector model with $g_{T5}$ coupling look virtually identical to the one with $g_T$ coupling and are therefore not shown.