Heavy Neutral Lepton at Same-Sign Muon Collider

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 $\mu$TRISTAN. The study focuses on two complementary HNL-mediated signatures: (i) the lepton-flavor-violating (LFV) channel $\mu^+\mu^+ \to W^+\tau^+\bar\nu_\mu$ 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 $\mu$TRISTAN collider with $\sqrt{s} \sim \mathcal{O}(10)~\text{TeV}$, 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.