Search for a New Gauge Boson in Electron-Nucleus Fixed-Target Scattering by the APEX Experiment

We present a search at the Jefferson Laboratory for new forces mediated by sub-GeV vector bosons with weak coupling ${\alpha }^{\prime }$ to electrons. Such a particle $A^{\prime }$ can be produced in electron-nucleus fixed-target scattering and then decay to an $e^{+}{e}^{-}$ pair, producing a narrow resonance in the QED trident spectrum. Using APEX test run data, we searched in the mass range 175–250 MeV, found no evidence for an $A^{\prime }\to e^{+}{e}^{-}$ reaction, and set an upper limit of ${\alpha }^{\prime }/\alpha \simeq {10}^{-6}$. Our findings demonstrate that fixed-target searches can explore a new, wide, and important range of masses and couplings for sub-GeV forces.

Figure 1

Top: (a) $A^{\prime }$ production from radiation off an incoming $e^{-}$ beam incident on a target consisting of nuclei of atomic number $Z$. APEX is sensitive to $A^{\prime }$ decays to $e^{+}{e}^{-}$ pairs, although decays to ${\mu }^{+}{\mu }^{-}$ pairs are possible for $A^{\prime }$ masses $m_{A^{\prime }}>2m_{\mu }$. Bottom: QED trident backgrounds: (b) radiative tridents and (c) Bethe-Heitler tridents.

Figure 2

The layout of the APEX test run. An electron beam (left-to-right) is incident on a thin tantalum foil target. Two septum magnets of opposite polarity deflect charged particles to larger angles into two vertical-bend high resolution spectrometers (HRS) set up to select electrons and positrons, each carrying close to half the incoming beam energy. The HRSs contain detectors to accurately measure the momentum, direction, and identity of the particles. Insertable sieve slit plates located in front of the septum magnets were used for calibration of the spectrometer magnetic optics.

Figure 3

Upper panel: The invariant mass spectrum of $e^{+}{e}^{-}$ pair events in the final event sample (black points, with error bars), accidental $e^{+}{e}^{-}$ coincidence events (blue short-dash line), and the QED calculation of the trident background added to the accidental event sample (red long-dash line). Lower panel: the bin-by-bin residuals with respect to a 10-parameter fit to the global distribution (for illustration only, not used in the analysis).

Figure 4

Top: Background-only model $p$-value versus $A^{\prime }$ mass. Middle: Shaded gray region denotes 90% confidence limit, 50% power-constrained allowed region [20]. 90% confidence upper limit is shown in solid blue (dotted blue) when it is above (below) the expected limit (gray dashed). The red solid line denotes the best fit for the number of signal events $S$. For comparison, the dot-dashed line indicates the contribution of statistical uncertainty to expected sensitivity, if the background shape were known exactly. Bottom: 90% confidence, 50% power-constrained, and expected limits as above, here quoted in terms of the ratio of signal strength upper limit to the QED background $B$ in a 1-MeV window around each $A^{\prime }$ mass hypothesis.

Figure 5

The 90% confidence upper limit on ${\alpha }^{\prime }/\alpha$ versus $A^{\prime }$ mass for the APEX test run (solid blue). Shown are existing 90% confidence level limits from the muon anomalous magnetic moment $a_{\mu }$ (fine hatched) [6], KLOE (solid gray) [12], the result reported by Mainz (solid green) [15], and an estimate using a BABAR Collaboration result (wide hatched) [2, 10]. Between the red line and fine hatched region, the $A^{\prime }$ can explain the observed discrepancy between the calculated and measured muon anomalous magnetic moment [6] at 90% confidence level. The full APEX experiment will roughly cover the entire area of the plot.