# Testing Non-Standard Neutrinos in Purely Leptonic Lepton Decays

## TL;DR

This paper introduces a novel method using polarization observables in purely leptonic decays to detect sterile neutrinos, highlighting distinctive signatures and singularities linked to sterile neutrino masses.

## Contribution

It proposes analyzing angular distributions and asymmetries in polarized decays to identify sterile neutrino signatures, emphasizing the potential of future collider experiments.

## Key findings

- Sterile neutrinos can cause singularities in asymmetry parameters.
- Distinctive signatures depend on sterile neutrino mass and decay kinematics.
- Polarized beams can improve sensitivity to sterile neutrino detection.

## Abstract

We propose a method to probe sterile neutrinos using polarization observables in the purely leptonic decays $\ell^{\prime-} \to \ell^{-} \bar{\nu}_{\ell} \nu_{\ell^{\prime}}$. By analyzing angular distributions and asymmetries derived from polarized decay rates, we identify distinctive signatures of sterile neutrino mixing. In particular, we demonstrate that sterile neutrinos can induce singularities in certain asymmetry parameters as functions of the invariant mass squared of the neutrino pair. These singularities occur for sterile neutrino masses $m_{4\nu}$ satisfying $m_{4\nu}^2 < m_{\ell^{\prime}}^2 / 2$, providing a clear target for experimental investigation. Our results motivate the incorporation of polarized beam sources at future colliders to enhance sensitivity to sterile neutrinos and other new physics.