Precision Rosenbluth Measurement of the Proton Elastic Form Factors

We report the results of a new Rosenbluth measurement of the proton electromagnetic form factors at $Q^2$ values of 2.64, 3.20, and $4.10{\mathrm{GeV}}^2$. Cross sections were determined by detecting the recoiling proton, in contrast to previous measurements which detected the scattered electron. Cross sections were determined to 3%, with relative uncertainties below 1%. The ratio ${\mu }_p{G}_E/G_M$ was determined to 4%–8% and showed ${\mu }_p{G}_E/G_M\approx 1$. These results are consistent with, and much more precise than, previous Rosenbluth extractions. They are inconsistent with recent polarization transfer measurements of similar precision, implying a systematic difference between the techniques.

Figure 1

The measured $\delta p$ spectrum for the low (top) and high (bottom) $\epsilon$ points at $Q^2=3.2{\mathrm{GeV}}^2$ (circles). The dotted magenta line is the background from the target walls, the long-dash green line is the simulated background from $\gamma p\to {\pi }^{0}p$ and $\gamma p\to \gamma p$ reactions, the short-dash blue line is the simulated elastic spectrum, and the solid red line (largely obscured by the data points) is the sum of the target wall, elastic, and background contributions.

Figure 2

Reduced cross sections as a function of $\epsilon$. The solid line is a linear fit to the reduced cross sections, the dashed line shows the slope expected from scaling (${\mu }_p{G}_E/G_M=1$), and the dotted line shows the slope predicted by the polarization transfer experiments [6].

Figure 3

Extracted values of ${\mu }_p{G}_E/G_M$ from this work (circles), a global analysis of previous cross section data (Fig. 2 of Ref. 12) (crosses), and high-$Q^2$ polarization transfer measurements [5, 6] (triangles).