Can a nonstandard invisible pair mimic the Michel distribution?

We ask whether a measured Michel distribution, apparently in excellent agreement with the Standard Model interpretation of the

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 ℓ i → ℓ j + X X ‾

for electrically neutral, color-singlet, mutually conjugate invisible pairs

X\bar X X X ‾

of spin up to

2 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 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. Phenomenologically, a subpercent branching fraction into this channel could bias the conventional muon-lifetime extraction of

G_F G F

upward by enough for the corrected value to agree with the CKM-unitarity determination, while increasing the discrepancy with the electroweak fit.