180 200 220 240 260 100 1000 10 4 10 5 10 6 10 7 10 8 e $^{+}$e$^{-}$mass H$_{MeV}$L Events GLYPH<144>H 1 MeV L 2 s 5 s 180 200 220 240 260 -$_{10 000}$ 0 10 000 20 000 30 000 40 000 50 000 e $^{+}$e$^{-}$mass H$_{MeV}$L Events GLYPH<144>H 1 MeV L H$_{Data}$ -$_{fit}$ L events in 6 days +$_{2}$s -$_{2}$s +$_{5}$s 10 6 evts 0.1 0.3 0.5 10 - 8 10 - 7 10 - 6 10 - 5 0.1 0.3 0.5 10 - 8 10 - 7 10 - 6 10 - 5 e $^{+}$e$^{-}$H$_{A’}$ L Mass H$_{GeV}$L a ’ GLYPH<144> a H 2 s sensitivity L Sensitivity of Proposed Run Plan C A D B FIG. 10: Anticipated 2 σ sensitivity in α $^{′}$/α = ϵ 2 for APEX [1] for the settings given in Table II (assuming a six-day run in configuration “A”, “C”, and “D” and a twelve-day run in “B”). Existing constraints are shown in the gray shaded re- gions. The colored curves correspond to the sensitivity in each of the individual energy settings, and the thick gray curve re- flects the sensitivity of a combined analysis. FIG. 11: Comparison of signal rates in six days of running at setting “A” to expected background and statistical sensitivity. Top: The resonances in purple and red lines correspond to A ′ signals at 200 MeV, smeared by a Gaussian to model detec- tor resolution and multiple scattering, with α $^{′}$/α = 6 . 5 × 10 − 6 and 1 . 3 × 10 − $^{7}$, respectively. The upper (purple) signal is just beyond the 2 σ expected sensitivity of a KLOE analysis, while the lower (red) signal corresponds to the “5 σ ” sensitivity (not including a trials factor) of this experiment. The gray line is the simulated invariant mass distribution for the continuum trident background, and the blue and green dashed lines re- flect the size of 2 and 5 σ Poisson fluctuations. Bottom: The gray line corresponds to the bin-by-bin differences between pseudodata containing no signal and a smooth fit to this pseu- dodata. Analogous subtractions when a signal is present are shown in purple and red, with the same α $^{′}$/α as in the top figure. Again the blue and green dashed lines reflect the size of 2 and 5 σ Poisson fluctuations. This paper summarized a new experiment (“ A ′ experi- ment ”, or “APEX”) that has been proposed to the Jeffer- son Laboratory’s PAC 35 [1]. The experiment proposes to use 30 days of beam to measure the electron-positron has α ′ /α = 1 . 3 × 10 − $^{7}$, corresponding to the expected “5 σ ” sensitivity (not accounting for the trials factor) in APEX. As a specific example, we have illustrated the expected sensitivity of setting “A” to A ′ signals with different ϵ in Figure 11. Each component of the target populates a different invariant mass distribution; for simplicity we consider only the contribution from the front planes of the target, with θ$_{eff}$ ≈ 5 . 5 ◦ (recall that the target is extended along the beam line and consists of 4–5 planes in a zig-zag configuration). The top panel illustrates the absolute size of A ′ signals at m$_{A}$ ′ = 200 MeV compared to the continuum trident background (gray line) and the size of 2 and 5-sigma statistical fluctuations (blue and green dashed lines), while the bottom panel illustrates how the same signals would appear after subtracting a smooth parameterization of the background. The purple curves in each panel corresponds to an A ′ signal with α ′ /α = 7 × 10 − 6 at 200 MeV, which according to the estimates in § II D would not be seen or excluded at 2 σ by a future KLOE search in φ → ηA ′ . The red curve 14 VIII. CONCLUSIONS In each setting, the proposed experiment will accumu- late between 70 and 300 million trident events. With these statistics, it will be possible to search offline for small resonances comprising a few thousandths of the collected data in a resolution-limited window. This will allow sensitivity to new gauge boson couplings α ′ /α as low as 10 − 7 over the broad mass range probed by APEX, as summarized in Figure 10. This sensitivity would im- prove on the cross-section limits from past experiments by a factor of ∼ 10 − 1000.