  The future high-energy muon colliders, featuring both high energy and low
background, could play a critical role in our searches for new physics. The
smallness of neutrino mass is a puzzle of particle physics. Broad classes of
solutions to the neutrino puzzles can be best tested by seeking the partners of
SM light neutrinos, dubbed as heavy neutral leptons (HNLs), at muon colliders.
We can parametrize HNLs in terms of the mass $m_N$ and the mixing angle with
$\ell$-flavor $U_\ell$. In this work, we focus on the regime $m_N > O(100)$ GeV
and study the projected sensitivities on the $|U_\ell|^2 - m_N$ plane with the
full-reconstructable HNL decay into a hadronic $W$ and a charged lepton. The
projected reach in $|U_\ell|^2$ leads to the best sensitivities in the TeV
realm.
