A. Brief overview of the experimental strategy B. Expected reach and impact experiment will provide a powerful probe for any new particle — vector, pseudo-vector, scalar, or pseudo-scalar — that has sub-GeV mass and couples to electrons (for other collider, accelerator, and direct and indirect as- trophysical probes see [5–25]; a proposal for an electron beam incident on a diffuse Hydrogen gas target using the Jefferson Laboratory’s Free Electron Laser has been discussed in [12]). APEX will be sensitive to new gauge bosons with cou- plings as small as α ′ /α ∼ (6 − 8) × 10 − 8 for masses in the range 65 − 300 MeV, and couplings as small as α ′ /α ∼ 2 × 10 7 for larger m$_{A}$ ′ ≲ 525 MeV. This is about a factor of ∼ 3 − 35 times lower in ϵ than exist- ing constraints (which assume that the A ′ couples also to muons), and corresponds to ∼ 10 − 1000 times smaller cross-sections. The precise mass range probed by this type of experi- ment can be varied by changing the spectrometer angu- lar settings and/or the beam energies. Thus, other ex- perimental facilities may be able to perform experiments similar to APEX, but targeting complementary regions of parameter space. The parameter range probed by APEX is interesting for several reasons. This region of mass and coupling is compatible with A ′ ’s explaining the annual modulation signal seen by the dark matter direct detection exper- iment DAMA/LIBRA, and also with dark matter an- nihilating into A ′ ’s, which explains a myriad of recent cosmic-ray and other astrophysical anomalies (see § II B). In addition, and independently of any connection to dark matter, the proposed experiment would be the first to probe A ′ s of mass ≳ 50 MeV with gauge kinetic mixing below ϵ ∼ 10 − $^{3}$, the range most compatible if the Stan- dard Model hypercharge gauge force is part of a Grand Unified Theory. The importance for fundamental physics of discovering new forces near the GeV scale cannot be overstated. The goal of the experiment is to measure the invari- ant mass spectrum of electron-positron pairs produced by electron scattering on a high- Z target, and search for a narrow peak with width corresponding to the instrumen- tal resolution. The electron and positron are detected in magnetic spectrometers with acceptance over a small range of particle momentum and angle, such that each ex- perimental setting is sensitive to a mass window ∼ ± 30% about a central mass value. Using four beam energies from 1–4 GeV, APEX will scan the e $^{+}$e − spectrum in the mass range 65 MeV to 550 MeV. Optimal sensitivity for these masses is achieved by studying symmetric e $^{+}$e − kinematics, where each particle carries approximately half the beam energy and has an opening angle ≈ 5 deg relative to the beam. Such small effective angles for the spectrometer can be achieved us- ing a septum magnet [1, 26]. Without a septum magnet, lower beam energies and correspondingly wider angles could be used to probe the same mass range. The impact of the geometry on the physics reach will be reviewed in § III and was discussed in detail in [3]. The experimental sensitivity is determined by statistics and mass resolution. Given the precision of spectrome- ters used, the latter is limited by multiple scattering in the target material. In APEX, a long, tilted wire mesh target is used to obtain excellent relative mass resolution of 0.5%. In addition, different segments of the target will enter the spectrometers for different central angles, in- creasing the size of mass window probed by each setting. With a beam of 80 µ A on 0.5%–10% radiation-length targets at various beam energies, we expect to collect true coincidence e $^{+}$e − events with a rate in the range 100–500 Hz (the expected background and accidental coincidence rates within a 2 ns timing window are about an order of magnitude lower). The total e $^{+}$e − sample size will exceed 10 8 pairs in a 6-day period for each setting, or a 12-day period for the 4 GeV setting. While this paper reflects an experimental setup opti- mized for the equipment in Hall A at JLab, many of the experimental considerations are also applicable for equip- ment available at the Mainz Microtron, JLab Hall B, and other experimental facilities. We consider new sub-GeV mass vector bosons — ‘dark photons’ A ′ — that couple very weakly to electrons 2 The paper is organized as follows. In § II, we present the physics of hypothetical A ′ particles, motivation for their existence, current limits, and estimated sensitivity for potential future analyses of existing data. In § III, we describe A ′ production in fixed-target experiments. In § IV, we describe the experimental setup. In § V, we present the parametrics and the Monte Carlo (MC) simu- lations of the QED e $^{+}$e − pair production rate and the A ′ signal rate in the proposed setup. We also describe how we made the sensitivity plots. Other background rates, such as π + or e + singles and accidental e $^{+}$e − pairs, are discussed in § VI. The expected sensitivity is discussed in § VII. The paper is summarized in § VIII. Three appen- dices discuss the form factors used to calculate the signal and background rates ( § A), the mass resolution ( § B), and the validation of the rates we obtain with the various MC simulations ( § C). II. PHYSICS C. The organization of this paper