Testing Non-Standard Neutrinos in Purely Leptonic Lepton Decays

TL;DR

This work proposes a polarization-based probe for sterile neutrinos in purely leptonic decays $\ell'^{-} \to \ell^{-} \bar{\nu}_{\ell} \nu_{\ell'}$, formulating the decay in a $Y$-frame and computing the polarized differential width with a Fierz-rearranged amplitude that includes active–sterile mixing through $U_{\ell j}$ and $U_{\ell' i}$. By constructing angular asymmetries $\Upsilon^S_{1,2,3}$ and their sterile corrections $\Delta\Upsilon_{1,2,3}$, the authors show that for $m_{4\nu}^2 < m_{\ell'}^2/2$ the new physics contribution produces singular behavior near $Y^2 \approx m_{\ell'}^2/2$, offering a distinctive signature in upcoming experiments. Numerical results for $m_{4\nu} = 0.1, 0.5, 1.0$ GeV reveal the sensitivity of $\delta\Upsilon_{\ell 2,3}$ to the sterile mass and mixing, with tau decays and polarized-beam colliders identified as particularly promising avenues. Overall, the study motivates developing polarized beams at future colliders to enhance tests of sterile neutrinos via polarization observables in leptonic decays.

Abstract

We propose a method to probe sterile neutrinos using polarization observables in the purely leptonic decays $\ell^{\prime-} \to \ell^{-} \barν_{\ell} ν_{\ell^{\prime}}$. 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 $m_{4ν}$ satisfying $m_{4ν}^2 < m_{\ell^{\prime}}^2 / 2$, 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.

Figures (2)

• Figure 1: Kinematics of the decay $\ell^{\prime-}\to \ell^-\bar{\nu}_\ell\nu_{\ell^{\prime}}$. The initial charged lepton $\ell^{\prime}$ has polarization $\zeta_{\ell^{\prime}}$. The angle $\theta_\ell$ is defined in the $\ell$ rest frame as the angle between the $\ell$ three-momentum and $\zeta_{\ell^{\prime}}$. The angle $\theta_\nu$ is defined in the $\bar{\nu}_\ell\nu_{\ell^{\prime}}$ center-of-mass frame as the angle between the three-momenta of $\bar{\nu}_\ell$ and $\nu_{\ell^{\prime}}$.
• Figure 2: Distributions of $\delta\Upsilon_{\ell1}$, $\delta\Upsilon_{\ell2}$, and $\delta\Upsilon_{\ell3}$ as functions of $Y^2$ in panels (I), (II), and (III), respectively. (a): $\tau^- \to \nu_\tau \mu \bar{\nu}_\mu$, (b): $\tau^- \to \nu_\tau e \bar{\nu}_e$. The Dark Blue, Teal, and Dark Red lines represent $m_{4\nu}=(0.1 ,0.5, 1.0) \text{GeV}$, respectively.