Collider limits on leptophilic interactions

Leptophilic interactions can only be observed at the LHC in four-lepton final states. If these interactions are mediated by a resonance in the di-leptonic channel with renormalizable couplings, the mediator must have spin 1. We study the LHC reach for such a vector boson allowing for arbitrary couplings. We find that only couplings to muons can be probed at the LHC because lepton flavor violating couplings are constrained by rare processes, couplings to electrons by LEP and the LHC is not sensitive to final states involving taus in this case. The ILC becomes then complementary to the LHC as it will provide the best limits on $Z'$ couplings to tau leptons. A prominent example is the case of the anomaly-free $Z'$ coupling to the muon minus tau lepton number ${\rm L}_\mu - {\rm L}_\tau$. If no departure from the Standard Model is observed at the LHC, the most stringent bounds on this vector boson are provided from events with only three charged leptons plus missing energy. Masses of the order of 1 TeV can be probed at the high-luminosity phase of the LHC for $Z^\prime$ couplings of order one. Generic four-lepton operators parametrizing leptophilic interactions can be also constrained using three and four (or two at the ILC) charged-lepton samples, but the corresponding limits are marginal, if meaningful, because the resonant behavior appears to be essential for the signal to be significant.