The bremsstrahlung-like production of the massive spin-2 dark matter mediator

The link between Standard Model (SM) particles and dark matter (DM) can be introduced via spin-2 massive mediator, \( {\text {G}}\), that couples to photon and charged leptons. Moreover, in a mediator mass range from sub-MeV to sub-GeV, fixed-target facilities such as NA64e, LDMX, NA64\(\mu \), \(\hbox {M}^3\), and E137, can potentially probe such particle of the hidden sector via the signatures that are described by the bremsstrahlung-like process involving tensor mediator. We compare numerically the Weizsaker–Williams (WW) approximation and the exact tree-level (ETL) method for the bremsstrahlung-like mediator production cross section by choosing various parameters of the fixed-target experiments. To be more specific, the determination of WW validity region (in the parameter space of spin-2 DM mediator scenario, that can be examined in the laboratory facilities) is of particular interest of the present manuscript. In addition, we derive novel constraints on spin-2 DM mediator parameter space from the data of the E137 fixed-target experiment. In particular, we demonstrate that the E137 experiment has been ruled out the couplings of the spin-2 mediator at the level of \(8~\times ~10^{-8}~\text{ GeV}^{-1}~\lesssim ~c^{\text {G}}_{ee}~\lesssim ~10^{-5}~\text{ GeV}^{-1}\) for the typical masses in the range \(100~\text{ MeV }~\lesssim ~m_{\text {G}}~\lesssim 800~\text{ MeV }\), that corresponds to the statistics of \(1.87~\times ~10^{20}\) electrons accumulated on target. The latter implies its universal coupling to photons and electrons, \(c^{\textrm{G}}_{\gamma \gamma }~=~c^{\textrm{G}}_{ee}\).