Status of the Zee-Babu model for neutrino mass and possible tests at a like-sign linear collider

We provide an updated scan of the allowed parameter space of the two-loop Zee-Babu model for neutrino mass. Taking into account most recent experimental data on $\mu\to e\gamma$ as well as the mixing angle $\theta_{13}$ we obtain lower bounds on the masses of the singly and doubly charged scalars of between 1 to 2 TeV, with some dependence on perturbativity and fine-tuning requirements. This makes the scalars difficult to observe at LHC with 14 TeV even with optimistic assumptions on the luminosity, and would require a multi-TeV linear collider to see the scalar resonances. We point out, however, that a sub-TeV linear collider in the like-sign mode may be able to observe lepton flavour violating processes such as $e^- e^- \to \mu^- \mu^-$ due to contact interactions induced by the doubly charged scalar with masses up to around 10 TeV. We investigate the possibility to distinguish the Zee-Babu model from the Higgs triplet model using such processes.