The Elusive Muonic WIMP

The Weakly Interacting Massive Particle (WIMP) paradigm is one of the most popular scenarios for Dark Matter (DM) theories that however is strongly constrained, in particular by direct detection experiments. We stick with the WIMP hypothesis and consider a Dirac fermion candidate for DM that interacts with the Standard Model (SM) via a spin-1 $Z'$, arising from the spontaneous breaking of an Abelian $U(1)'_{\mu}$ gauge symmetry, under which only second generation leptons and the DM are appropriately charged. Due to the charge assignment, the model is gauge anomalous and can only be interpreted as an effective field theory (EFT) at low energy. The $Z'$ couples at tree level only to the vector DM current, to the axial muon current and to left-handed muonic neutrinos, so the WIMP-nucleon cross section is beyond the experimental reach of spin-independent (SI) direct detection searches. We study the current bounds on this model coming from direct and indirect detection of DM, collider searches, contributions to $(g-2)_{\mu}$ and to neutrino trident production. We find that large regions of the parameter space remains to be explored. In the context of LHC searches, we study the impact of a muon-exclusive signal region for the $3\mu$ + ${E}^{{\rm miss}}_T$ channel with an invariant mass window around $m_{Z'}$. We show that this search can significantly improve the current collider bounds. Finally, from the anomalous nature of our EFT, there remain at low energy triboson anomalous interactions between the $Z'$ and the electroweak (EW) SM gauge bosons. We explore the possibilities of probing these interactions at the LHC and at a 100 TeV proton collider finding it extremely challenging. On the other hand, for a muon collider the resonant channel $\mu^{+}\mu^{-}\to Z'\to ZZ$ could be discovered in the most promising scenario with luminosity of $\mathcal{O}({\rm few}\; 10)$ ${\rm fb}^{-1}$.