Looking forward to photon-coupled long-lived particles I: massive spin-2 portal

A massive spin-2 particle, $G$, can provide the expected link between the Standard Model and the Dark Sector. In this work, we consider for the first time such a state as a $\sim\,$sub-GeV long-lived particle that decays predominantly into a photon pair, e.g., due to a dimension-5 coupling $g_{\gamma\gamma}$. We show that it can be efficiently searched at the future beam dump experiments and at the LHC, such as: FASER2, Forward Physics Facility, MATHUSLA, NA62, SeaQuest, and SHiP, while current constraints come from BaBar, CHARM, and NuCal. We consider two cases: universal coupling of $G$ to the SM gauge and matter fields - leading to a phenomenology similar to that of an axion-like particle - and photophilic coupling which leads to perturbative unitarity violation for $m_G \lesssim 50\,\mathrm{MeV}$. In both cases, the Primakoff-like coherent upscattering of an on-shell photon hitting heavy nuclei of the beam target provides the dominant $G$ production mode. We find that SHiP will provide the strongest constraint, $g_{\gamma\gamma} \lesssim 4.8 \times 10^{-8} \,\mathrm{GeV}^{-1}$ ($g_{\gamma\gamma}\lesssim 3.6 \times 10^{-8} \,\mathrm{GeV}^{-1}$) for $m_G=1 \,\mathrm{GeV}$ in the case of universal (photophilic) coupling, while the rest of experiments will cover $m_G \lesssim 0.5\,\mathrm{GeV}$, $g_{\gamma\gamma}\gtrsim 7 \times 10^{-7} \,\mathrm{GeV}^{-1}$ ($m_G \lesssim 0.6\,\mathrm{GeV}$, $g_{\gamma\gamma}\gtrsim 6 \times 10^{-7} \,\mathrm{GeV}^{-1}$) region of the parameter space.