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 KTeV KLOE Belle FIG. 3: Anticipated 2 σ sensitivity in α $^{′}$/α = ϵ 2 for the A ′ experiment (APEX) at Hall A in JLab (thick blue line), com- pared with current limits and estimated potential 2 σ sensi- tivity for A ′ searches in existing data (dashed lines), assum- ing optimal sensitivity as described in the text. From left to right: KTeV π 0 → γA ′ → γe $^{+}$e − (orange dashed curve), KLOE φ → ηA ′ → ηe $^{+}$e − (green dashed curve) and Belle e $^{+}$e − → γA ′ → γµ $^{+}$µ − (gray dashed curve). Existing con- straints are as in Figure 1. D. Sensitivity of Potential Searches using Existing Data constraint to represent a 95% C.L. upper bound, we find the constraint depicted in Figure 1. For m$_{A}$ ′ ≳ 2 m$_{µ}$ , this requires α ′ /α ≳ 10 − $^{5}$, while the constraint weakens at higher masses, especially near the ρ -resonance. See [87] for a comparison of our sensitivity estimate to those previously published. We caution that systematic uncertainties in the A ′ limit beyond those quoted in [75] may slightly weaken the resulting limit, which should therefore be taken as a rough approximation unless further analysis is done. First, A ′ production in B-factories is more forward- peaked than the Υ(3 S ) decay mode considered in [75], so that the signal acceptance is more uncertain. In ad- dition, background distributions in [75] are derived from smooth polynomial fits to data collected on the Υ(4 S ) resonance, which is assumed to contain no signal. This assumption is not correct for A ′ production, though the resulting systematic effects are expected to be small. Several past and current experiments have data that could be used to significantly improve current limits on α ′ /α , as discussed in [4, 8, 27]. Here, we esti- mate the potential sensitivity of searches in three chan- nels ( π 0 → γA ′ → γe $^{+}$e − , φ → ηA ′ → ηe $^{+}$e − , and e $^{+}$e − → γA ′ → γµ $^{+}$µ − ), considering only the statis- tical uncertainties and irreducible backgrounds. These are likely overestimates, as we are unable to include ei- ther systematic uncertainties or significant instrumental backgrounds such as photon conversion in the detector volume. muon threshold, φ decays are not competitive with B - factory continuum production. In addition, BaBar and Belle can search for the con- tinuum production mode e $^{+}$e − → γA ′ → γµ $^{+}$µ − in their full datasets. For example, an analysis of the Belle Υ(4 S ) data set would increase statistics by a factor of ∼ 24 rela- tive to the BaBar Υ(3 S ) search that we have interpreted as a limit above. We have derived the expected sensi- tivity (shown as a black dashed line in Figure 3) simply by scaling the Υ(3 S ) estimated reach by √$_{24.}$ These searches have not been extended below the muon thresh- old because of large conversion backgrounds. BaBar, BELLE, and KTeV (E799-II) have produced and detected large numbers of neutral pions, of order 10 $^{10}$, of which roughly 1% decay in the Dalitz mode π 0 → e $^{+}$e − γ . These experiments can search for the decay π 0 → γA ′ induced by A ′ –photon kinetic mix- ing, which would appear as a narrow resonance over the continuum Dalitz decay background. KTeV has the largest π 0 sample, and its e $^{+}$e − mass resolution can be approximated from the reported measurement of the π 0 → e $^{+}$e − branching fraction [76] to be roughly 2 MeV. This paper also reports the measured mass distribution of Dalitz decays above 70 MeV, from which we estimate potential sensitivity to α ′ /α as small as 5 × 10 − 7 for 70 < m ( e $^{+}$e − ) ≲ 100 MeV, as shown by the orange shaded region in Figure 3. Similarly, KLOE can search for the decay φ → ηA , likewise induced by A ′ kinetic mixing with the photon, in a sample of 10 10 φ ’s. An analysis of this data is ongoing [77]. We have taken the blue dashed curve in Figure 3 from [4], which assumes that mass resolution σ$_{m}$ is dominated by KLOE’s 0 . 4% momentum resolution. We have adjusted the contours from [4] to determine a 2 σ contour and enlarged the bin width used to determine signal significance from σ$_{m}$ in [4] to 2 . 5 σ$_{m}$ . Above the A ′ particles are generated in electron collisions on a fixed target by a process analogous to ordinary photon bremsstrahlung, see Figure 4. This can be reliably es- timated in the Weizs¨ acker-Williams approximation (see [3, 78–80]). When the incoming electron has energy E$_{0}$ , the differential cross-section to produce an A ′ of mass III. A ′ PRODUCTION IN FIXED TARGET INTERACTIONS 7