Testing tree level TeV scale seesaw scenarios in $\mu$TRISTAN

We investigate TeV scale seesaw scenarios at $\mu^+ e^-$ and $\mu^+ \mu^+$ colliders in the $\mu$TRISTAN experiment. In minimal type-I seesaw scenario we consider two generations of Standard Model (SM) singlet heavy Majorana type Right Handed Neutrinos (RHNs) which couples with SM gauge bosons through light-heavy neutrino mixing. We discuss the prospects of probing heavy neutrinos via the processes such as $\mu^+e^-\to \nu N_i\to e^+ j j\nu$ or $\mu^- j j\nu$ for $\sqrt{s}=346$~GeV and $1\text{ ab}^{-1}$ luminosity. Studying these process, we estimate limits on the light-heavy neutrino mixing angles as a function of heavy neutrino mass, which could be two orders of magnitude stronger than electroweak precision data. Further, we study the effect of doubly charged scalar boson $(H^{++})$ from the type-II seesaw scenario in $\mu^+ \mu^+$ collision at $\sqrt{s}=2$ TeV. In this case we consider $\mu^+ \mu^+ \to \ell_i^+ \ell_j^+$ and $\mu^+ \mu^+ \to H^{++} Z/ \gamma$ processes followed by the same sign dilepton decay of $H^{++}$. We find that events involving $e^+ e^+$ among these final states can probe the neutrino mass ordering in $\mu$TRISTAN experiment at 5$\sigma$ significance. In addition to that we study the production of positively charged triplet fermion in $\mu$TRISTAN following $\mu^+ \mu^+ \to \mu^+ \Sigma^+$ process where $\Sigma^+$ decays into $\mu^+ jj$ mode through $Z$ boson exchange. Considering a triplet at 1 TeV and studying SM backgrounds we estimate the discovery potential of $\mu^+ \mu^+ jj$ signal at $\mu$TRISTAN with respect to projected luminosity.