First Measurement of the $Q^2$ Dependence of the Beam-Normal Single Spin Asymmetry for Elastic Scattering off Carbon

We report on the first $Q^2$-dependent measurement of the beam-normal single spin asymmetry $A_n$ in the elastic scattering of 570 MeV vertically polarized electrons off ${}^{12}\mathrm{C}$. We cover the $Q^2$ range between 0.02 and $0.05{\mathrm{GeV}}^2/c^2$ and determine $A_n$ at four different $Q^2$ values. The experimental results are compared to a theoretical calculation that relates $A_n$ to the imaginary part of the two-photon exchange amplitude. The result emphasizes that the $Q^2$ behavior of $A_n$ given by the ratio of the Compton to charge form factors cannot be treated independently of the target nucleus.

Figure 1

The excitation energy spectrum shows the acceptance of the spectrometer without Cherenkov cut (black line) and of the Cherenkov detector only (shaded area). By changing the magnetic field of the spectrometer, the elastic peak was moved until it matched the position of the Cherenkov detector.

Figure 2

(Top panel) Comparison between the asymmetry in the integrated signal from a beam-current monitor observed in a run with beam stabilization off (red) and with beam stabilization on (black). (Bottom panel) Raw asymmetry determined for one PMT of the Cherenkov detector in spectrometer $B$ as a function of the current asymmetry for a run without beam stabilization.

Figure 3

The transverse asymmetry $A_{\exp }$ for each PMT of the detectors placed in spectrometer $A$ (filled red circles) and spectrometer $B$ (open blue circles) at $Q^2=0.04{\mathrm{GeV}}^2/c^2$. By inserting an additional $\lambda /2$-wave plate into the laser beam of the polarized electron source, the general sign changed.

Figure 4

Extracted transverse asymmetries $A_n$ for the detectors placed in spectrometer $A$ (filled red circles) and spectrometer $B$ (open blue circles) versus $Q^2$. The width of the given boxes indicates the full width at half maximum of the $Q^2$ distribution, which is determined by the intersection of the angular acceptance of the spectrometers and the geometry of the detectors. The statistical and systematic uncertainties are given by the error bars and the height of the boxes, respectively. The theoretical calculation for $E_b=0.570\mathrm{GeV}$ of Ref. [24] (black line) is shown for comparison. The given bands belong to the uncertainty of the Compton slope parameter of 10% (light grey) and 20% (dark grey). In addition, the result of the PREX Collaboration (black diamond) at $E_b=1.063\mathrm{GeV}$ [18] is shown.