Probing hidden spin-2 mediator of dark matter with NA64e , LDMX, NA64μ , and M3

Abstract

The connection between Standard Model (SM) particles and dark matter (DM) can be introduced via a hidden spin-2 massive mediator. In the present paper we consider the simplified benchmark link between the charged lepton sector of SM and DM particles, which are considered to be hidden Dirac fermions from the dark sector. The regarding couplings are established through the dimension-five operators involving spin-2 mediator field and the energy-momentum tensors of both SM and DM sectors. We study in detail the implication of this scenario for the lepton fixed-target facilities, such as $\mathrm{NA}64e$, LDMX, $\mathrm{NA}64\ensuremath{\mu}$, and ${\mathrm{M}}^{3}$; in particular, for the specific experiment we discuss in detail, the missing energy signatures of spin-2 boson production followed by its invisible decay into stable DM pairs. Moreover, we derive the expected reaches of these experiments for the projected statistics of the leptons accumulated on the target. We also discuss the implication of both nuclear and atomic form-factor parametrizations for the differential spectra of hidden spin-2 boson emission, the total cross section of its production, and the experimental reach of the fixed-fixed-target facilities for probing hidden spin-2 DM mediator. We briefly discuss the DM relic abundance parameter space that can be probed by these experiments.