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, 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$\mu$, 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) approach for the bremsstrahlung-like mediator production cross section by choosing various parameters of the fixed-target experiments. 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 the couplings of the spin-2 mediator at the level of $8\times {10}^{-8}Ge{V}^{-1}\lesssim c_{ee}^{\mathrm{G}}\lesssim {10}^{-5}Ge{V}^{-1}$ for the typical masses in the range $100MeV\lesssim m_{\mathrm{G}}\lesssim 800MeV$, that corresponds to the statistics of $1.87\times {10}^{20}$ electrons accumulated on target. The latter implies its universal coupling to photons and leptons, $c_{ee}^{\mathrm{G}}=c_{\gamma \gamma }^{\mathrm{G}}$.