Can a Nonstandard Invisible Pair Mimic the Michel Distribution?

TL;DR

This paper investigates whether a nonstandard invisible sector, specifically a massless complex scalar pair, can mimic the Michel distribution in lepton decays, potentially hiding new physics in standard measurements.

Contribution

It identifies a unique nonstandard invisible sector that can produce Michel distribution patterns indistinguishable from the Standard Model in lepton decays.

Findings

A massless complex scalar pair with a left-handed vector current reproduces the Michel distribution.

Higher-spin invisible pairs produce distinguishable kinematic signatures.

The study isolates the only nonstandard invisible sector that can hide in Michel decay measurements.

Abstract

We ask whether a measured Michel distribution, apparently in excellent agreement with the Standard Model interpretation of the $\ell_i \to \ell_j \nu\bar\nu$ decay, could instead arise from a different invisible sector. Within a general low-energy effective field theory, we analyze lepton decays $\ell_i \to \ell_j + X\bar X$ for electrically neutral, color-singlet, mutually conjugate invisible pairs $X\bar X$ of spin up to $2$, allowing (pseudo)scalar, (axial)vector, and antisymmetric tensor interactions in the lepton current, focusing on the massless limit relevant for exact degeneracies. We formulate a criterion for indistinguishability based on the full set of measurable differential distributions. Under these assumptions, besides the obvious spin $1/2$ case, there is a unique nontrivial solution: a massless complex scalar pair coupled through a purely left-handed vector current exactly reproduces the standard Michel pattern, including its extensions to daughter-lepton polarization and radiative channels. All other cases studied here are distinguishable, in particular because higher-spin invisible pairs produce additional kinematic prefactors. These results isolate the only nonstandard and nontrivial invisible sector that can remain hidden in Michel-type lepton decay measurements.