We explore the discovery potential of heavy neutral leptons (HNLs), motivated by models addressing the origin of neutrino masses, at the proposed high-energy same-sign muon collider known as $\mu \mathrm{TRISTAN}$. The study focuses on two complementary HNL-mediated signatures: (i) the lepton-flavor-violating (LFV) channel ${\mu }^{+}{\mu }^{+}\to W^{+}{\tau }^{+}{\overline{\nu }}_{\mu }$ and (ii) the lepton-number-violating (LNV) channel ${\mu }^{+}{\mu }^{+}\to W^{+}{W}^{+}$. The LNV process is the muon analogue of inverse neutrinoless double beta decay and, if observed, would provide strong evidence for Majorana neutrinos, while the LFV process offers a novel probe of flavor-changing neutral currents in the lepton sector. At the $\mu \mathrm{TRISTAN}$ collider with $\sqrt{s}\sim \mathcal{O}(10)\mathrm{TeV}$, the resulting sensitivity to the HNL mixing with muon and tau neutrinos, as a function of mass, can surpass current bounds from the measurements of electroweak precision observables over a broad mass range. In particular, for the mixing with muon neutrinos, the collider bound can improve by an order of magnitude for 5–10 TeV HNLs.

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• Extensions of fermion sector
• Phenomenology