Illuminating sequential freeze-in dark matter with dark photon signal at the CERN SHiP experiment

Single-field freeze-in dark matter barely leaves observable footprints in dark matter direct detection, collider, or fixed-target experiments, which can be altered in the two-field context. In this work, we consider sequential freeze-in dark matter through signals of a dark photon mediator with a mass range of m A ′ ∼ 10 − 2 – 10 GeV covered by the proposed SHiP experiment. We show that the dark charge is fixed to be e ′ ∼ 1.3 × 10 − 12 and the mixing parameter is restricted to 10 − 11 ≤ ε < 10 − 8 – 10 − 7.5 , as a result of the out-of-equilibrium condition of dark photon and the observed relic abundance of dark matter. Within this ε region, the 5-yr (15-yr) data of the proton bremsstrahlung process for the dark photon, assuming vector meson (dipole) dominance, excludes ε ≥ 10 − 8.5 ( 10 − 7.9 ) at 90% confidence level, implying only a narrow region of ε close to ∼ 10 − 11 left for alternative tests.