Lepton number violating signals of a parity symmetric model at $\mu$TRISTAN

The parity solution to the strong CP problem necessarily extends the Standard Model to include the SU$(2)_{\rm R}$ gauge sector and imposes restrictions on the structure of the Yukawa interactions. In this framework, one can consider an appealing structure of the neutrino sector in which the smallness of the neutrino masses is naturally explained, while lepton number symmetry is substantially violated at the TeV scale. Observation of distinctive lepton number violating signals at collider experiments can therefore be expected, since the rates are not suppressed by the small neutrino masses. We study the constraints from neutrinoless double beta decay and discuss the prospects for discovering new TeV-scale particles, such as the $W'$ boson of SU$(2)_{\rm R}$, via lepton number violating processes at a $\mu^+ \mu^+$ collider, $\mu^+ \mu^+ \to W^+ W'^+$. A $\mu^+ \mu^+$ collider with a center-of-mass energy of 10 TeV can probe the $W'$ boson mass up to about 10 TeV through on-shell production, and the reach can extend to 16 TeV by studying processes involving off-shell $W'$ boson.