Vectorlike leptons and long-lived bosons at the LHC

We study a renormalizable theory that includes a heavy weak-singlet vectorlike lepton, $\tau^\prime$, that decays into a pseudoscalar boson and a tau lepton. We show that this can be the dominant decay mode of $\tau^\prime$ provided the pseudoscalar couplings deviate from the case of a Nambu-Goldstone boson. For a range of parameters, the pseudoscalar is long-lived, and mainly decays into a photon pair at one loop, or into a tau pair at tree level. Electroweak production of $\tau^{\prime +} \tau^{\prime -}$ leads to a rich phenomenology at colliders, including signals with many taus or photons. We analyze in detail the LHC signal involving two prompt taus and two displaced photon pairs. Particularly interesting is the case where the pseudoscalar has a decay length of a few meters and thus would typically deposit energy in the muon chambers of the CMS or ATLAS detectors.