0.0 0.2 0.4 0.6 0.8 0.05 0.10 0.50 1.00 5.00 10.00 e $^{+}$e$^{-}$pair mass H$_{GeV}$L c GLYPH<144> Z 2 , Tungsten 0.0 0.2 0.4 0.6 0.8 0 1 2 3 4 5 e $^{+}$e$^{-}$pair mass H$_{GeV}$L Ratio of s* Lumi Si to W where δ$_{θ}$ is the angular resolution of the electron or positron, and δ$_{p}$/p is the momentum resolution of the HRS, which is always less than 3 × 10 − 4 (in our esti- mates for the reach of ϵ , we take δp/p to be equal to this upper bound). We have where δ$_{HRS}$ is the HRS angular resolution, which is ∼ 0 . 5 mrad in the horizontal direction and ∼ 1 mrad in the ver- tical direction. Moreover, δ ms θ represents the degradation of the resolution due to multiple Coulomb scattering in the target. It is given by the standard formula [81] where t is the thickness in radiation lengths of the ma- terial along the path of the particle, X$_{0}$ is the radiation length of the target in g/cm $^{2}$, and p is the momentum of particle in MeV. For the proposed experiment, the thickness of the tar- get along the direction of the beam line varies from t = 0 . 003 X$_{0}$ to t = 0 . 09 X$_{0}$ . However, in the case of a foil target or a target composed of several thin wires, the distance traversed by trident electron-positron pairs can be significantly smaller because the electron and positron have relatively large angles with respect to the beam line. For a foil, we can take t ≈ 1 $_{2}$t$_{f}$ / sin( θ$_{p}$ − θ$_{f}$ ), where t$_{f}$ is the foil thickness and θ$_{f}$ its angle relative to the beam line. In this case the effective thickness traversed by the beam is T$_{0}$ = t$_{f}$ / sin θ$_{f}$ . In the case of a target composed of multiple wires, as was assumed in determining the experimental sensi- tivity, the wires can be spaced widely enough that the pair-produced particles need only travel through a sin- gle wire. In this case, t is typically the radius of the wire, which for Tungsten wire targets can be as small as 10 µ m, or 3 × 10 − $^{3}$X$_{0}$ . In this case, we find that the HRS angular resolution, δ$_{HRS}$ , is comparable to the multiple scattering δ ms θ in the proposed experiment. In this appendix, we briefly describe an estimate of the mass resolution of the spectrometer. Since we are looking for a small bump on the invariant mass spectrum distribution, an excellent mass resolution is essential to obtain a good reach in ϵ . The mass resolution of the spectrometer, δ$_{m}$ , is roughly given by We first discuss a comparison of the MC with previous experimental results from the JLab experiment E04-012 [86]. This experiment consisted of a 5.01 GeV, 14 . 5 µA electron beam incident on a 1.72% radiation length liquid Hydrogen target. The e + singles rate was measured to be ∼ 1 . 1 kHz in a momentum window of ± 4% around 1.93 GeV and an angular acceptance of 4.5 msr with an aspect ratio of 2-to-1 centered at an angle of 6 ◦ . The e $^{+}$e − coin- cidence rate was measured at ∼ 4 Hz for the same angular In this appendix, we briefly describe a validation of the Monte Carlo (MC) simulation of the signal, Bethe-Heitler and radiative trident backgrounds (shown in Figure 8 and discussed in § V), and the positron singles. $^{(}$δ$_{m}$ m$^{)}$$^{2}$ =$^{(}$ δ$_{p}$ p ) 2 + 0 . 5 ×$^{(}$ δ$_{θ}$ θ ) 2 , (B1) R ( Z$_{1}$, Z$_{2}$ ) = X$_{0}$ ( Z$_{1}$ ) χ ( Z$_{1}$, t ) /A ( Z$_{1}$ ) X$_{0}$ ( Z$_{2}$ ) χ ( Z$_{2}$, t ) /A ( Z$_{2}$ ) . (A5) Appendix C: Monte Carlo validation with E04-012 data Appendix B: Mass resolution For example the ratio R ( Si, W ) is shown in the right panel of Figure 12, again as a function of e $^{+}$e − mass for beam energies between 1 and 4 GeV. 16 by the ratio FIG. 12: Top: The factor ˜ χ = χ/Z 2 defined in (A2) and (A1) as a function of e $^{+}$e − mass for (bottom to top) 1, 2, 3, and 4 GeV incident electrons on a Tungsten target. Bottom: The ratio of (A5) A ′ production rates per radiation length for Silicon and Tungsten targets, as a function of invariant mass and for beam energies (top to bottom at 0.4 GeV) 1, 2, 3, and 4 GeV incident electrons. ( δ$_{θ}$ ) 2 = ( δ$_{HRS}$ ) 2 + ( δ ms θ ) $^{2}$, (B2) δ ms θ = 13 . 6 p [MeV]$^{√}$ t X$_{0}$ [ 1 + 0 . 038 ln ( t X$_{0}$$^{)}$$^{]}$ , (B3)