Experimental investigation of strong field trident production

We show by experiment that an electron impinging on an electric field that is of critical magnitude in its rest frame, may produce an electron-positron pair. Our measurements address higher-order QED, using the strong electric fields obtainable along particular crystallographic directions in single crystals. For the amorphous material our data are in good agreement with theory, whereas a discrepancy with theory on the magnitude of the trident enhancement is found in the precisely aligned case where the strong electric field acts.

Figure 1

A schematical drawing—not to scale—of the setup used in the experiment. The total length is about 65 m.

Figure 2

SSD spectra for the $170\mu \mathrm{m}$ Ge $⟨110⟩$ crystal obtained under axially aligned conditions (blue dashed line), under “random” alignment (red dotted) and without target (green dash-dotted). The full line (with an average over 10 channels and multiplied by ${10}^3$) shows events in the SSD which have three hits in either DC5 or DC6 and 3 or 2 in the other. The peak around channel 1100 is identified as trident events.

Figure 3

Comparison between the nominal momentum of the tertiary electron beam and the momentum/energy measured in the PS (open symbols, dotted line) LGC (full symbols, solid line) including least-squares linear fits.

Figure 4

Correlation between projection of electron track into the center of the MDX magnet, $x_p$, and $x_v$.

Figure 5

Distribution of $z$-vertex coordinates. The MDX was located with its center at $z=5840\mathrm{cm}$, with a length of 40 cm.

Figure 6

Comparison between the LGJ calorimeter and the trident positron momentum found with the PS.

Figure 7

Comparison between pair production data and simulation (with a normalized vertical scale).

Figure 8

Experimental (filled squares) and simulated (full line) trident production in the “random” configuration of the $170\mu \mathrm{m}$ thick Ge $⟨110⟩$ crystal.

Figure 9

Detection efficiency found from simulation.

Figure 10

Enhancements within narrow windows of SSD channels for the $170\mu \mathrm{m}$ (filled dots) and $400\mu \mathrm{m}$ (open squares) thick crystals. For comparison, the SSD spectrum for the $400\mu \mathrm{m}$ thick crystal at axial alignment and with all trident selection cuts is shown as a line.

Figure 11

Trident positron spectra for $170\mu \mathrm{m}$ and $400\mu \mathrm{m}$ thick Ge crystals in the “random” orientation. The energy of the primary particle is $E_0=180\mathrm{GeV}$. The dashed line shows the calculated photon contribution, the dotted line the theoretical expectation according to Baier and Katkov [16] and the solid line shows the sum of these contributions. The filled dots are experimental data corrected for the detection efficiency shown in Fig. 9.

Figure 12

Trident positron spectra for the $170\mu \mathrm{m}$ thick Ge crystal in the $⟨110⟩$ axial orientation (upper graph) and for the $400\mu \mathrm{m}$ thick Ge crystal at an angle of $\simeq 0.3$ to the axis (lower graph). The energy of the primary particle is $E_0=180\mathrm{GeV}$. The dashed line shows the calculated photon contribution, the dotted line the theoretical expectation for precise alignment according to Baier and Katkov [35] and the solid line shows the sum of these contributions. The filled squares are experimental data corrected for the detection efficiency shown in Fig. 9.

Figure 13

Enhancements for the $170\mu \mathrm{m}$ thick crystal and the $400\mu \mathrm{m}$ thick crystal, compared to theory according to [35].

Figure 14

Differential enhancement of trident production as a function of the momentum of the produced positron (filled squares) and as a function of the momentum of the produced electron (open circles). The points show results obtained for 180 GeV electrons penetrating a) a $170\mu \mathrm{m}$ Ge $⟨110⟩$ crystal aligned axially and b) a $400\mu \mathrm{m}$ Ge $⟨110⟩$ crystal at an angle of $\simeq 0.3\mathrm{mrad}$ to the axis.

Figure 15

Differential enhancement of trident production as a function of the momentum of the produced electron. The points show results obtained for 125 (open triangles), 180 (filled squares) and 210 GeV (open circles) electrons penetrating a $400\mu \mathrm{m}$ Ge $⟨110⟩$ crystal at an angle of $\simeq 0.3\mathrm{mrad}$ to the axis.