Probing TeV scale origin of neutrino mass at future lepton colliders via neutral and doubly-charged scalars

We point out how future lepton colliders can provide unique insight into the scalar sector of TeV scale models for neutrino masses with local $B-L$ symmetry. Our specific focus is on the TeV scale left-right model, which naturally embeds this $B-L$ symmetry. In particular, we make a detailed study of the lepton collider implications of the neutral ($H_3$) and doubly-charged ($H^{\pm \pm }$) scalars from the right-handed triplet Higgs that is responsible for the spontaneous breaking of the $B-L$ symmetry and implementing the seesaw mechanism. Due to mixing with other scalars, the neutral scalar $H_3$ could acquire sizable flavor violating couplings to the charged leptons. Produced on-shell or off-shell at the planned $e^{+}{e}^{-}$ colliders, it would induce distinct lepton flavor violating signals like $e^+e^- \to \mu^\pm \tau^\mp ~ (+H_3)$,withthecouplingsprobedupto$\sim 10^{-4}$ for a wide range of neutral scalar mass, which is well beyond the reach of current searches for charged lepton flavor violation. The Yukawa couplings of the doubly-charged scalar $H^{\pm \pm }$ to the charged leptons might also be flavor-violating, which is correlated to the heavy right-handed neutrino masses and mixings. With a combination of the pair, single and off-shell production of $H^{\pm \pm }$ like $e^{+}{e}^{-}\to H^{++}{H}^{--},H^{\pm \pm }{e}^{\mp }{\mu }^{\mp },{\mu }^{\pm }{\tau }^{\mp }$, the Yukawa couplings can be probed up to ${10}^{-3}$ at future lepton colliders, which is allowed by current lepton flavor data in a large region of parameter space. For both the neutral and doubly-charged cases, the scalar masses could be probed up to the few-TeV range in the off-shell channel.