Introduction

The structure of the proton is a matter of universal interest in nuclear and particle physics. Charge and current distributions are obtained through measurements of the electric and magnetic form factors, G_E and G_M, and so it is extremely important to determine these quantities as accurately as possible. The form factors are a function of the square of the four-momentum transfer, Q², and can be separated out by measuring the e-p elastic scattering cross section at two values of the virtual photon polarization parameter, $\epsilon$, i.e. by performing a Rosenbluth separation. Several such measurements have been reported [1,2] and the results are shown in figure 1, expressing G_M in units of the magnetic moment of the proton $\mu_p$ (as is done throughout this proposal). Global fits [1,3] to these data find that G_E/G_M = 1 to within 0.1 with no significant Q²-dependence. While no experiment strongly disagrees with a constant value of G_E/G_M, the measurements show somewhat inconsistent trends. Procedures for radiative corrections have improved since the earlier experiments ran, but the radiative corrections were redone for the global analysis. In addition, for Q² < 3.5 GeV², removing any single L-T measurement from the global analysis does not significantly change the result. Above Q²=3.5 GeV², only the NE11 experiment (solid circles in figure 1) has high precision data.

  

Figure: $\mu_pG_E/G_M$ as deduced from Rosenbluth separation measurements from SLAC, DESY, and CEA [1,2].

A recent experiment in Hall A [4] measured G_E/G_M by polarization transfer and found that G_E/G_M decreases with increasing Q² above Q²=1 GeV², reaching a value of 0.6 at the highest Q² measured (see figure 2). This polarization transfer measurement is less prone to systematic issues than the L-T measurements and quotes significantly smaller uncertainties. The new results are clearly inconsistent with a constant value of G_E/G_M=1, as favored by the global analysis of the L-T measurements. In fact, the Hall A results are consistent with only one of the four L-T measurements with data above Q²=2 GeV². Additional data is being taken in Hall A that will extend this measurement up to Q²=5.6 GeV². The new Hall A results not only gives us a different picture for the Q²-dependence of G_E/G_M, but also brings into question the SLAC L-T measurements. This impacts not only our understanding of the proton electric form factor, but may also impact other L-T measurements if there are a energy-dependent systematic uncertainties that have not been taken into account. An independent measurement of G_E/G_M in the region where we can achieve uncertainties comparable to or better than the Hall A measurement will be an important as a check on the value of G_E/G_M, and on the possibility of additional systematic uncertainties in the L-T or polarization transfer measurements. As the polarization transfer technique can be extended to large values of Q², where the L-T separation becomes increasingly difficult, it is important to have a precise comparison of the two techniques in the region where both can extract G_E/G_M with high precision.

  

Figure: $\mu_pG_E/G_M$ as deduced from polarization transfer [4] (closed circles) and a global analysis of L-T separation measurements [1] (open circles).

We propose to measure G_E/G_M for the proton in a region where the previous determinations differ well outside of experimental uncertainties by utilizing the L-T separation technique in a new way in which only ratios of cross sections are used. Because of this the results are independent of target thickness and beam intensity and quite insensitive to uncertainties in beam energy. Protons rather than the usual electrons will be counted which reduces the variation with scattering angle, reduces the size of the radiative corrections and has the added advantage that the proton energy depends only on Q². Counting rates are high and a statistical accuracy of less than 0.3% can be achieved in less than a day of data taking at each point. We propose to take one-, two-, three-, and five- pass data with a fixed linac energy and in a total of 10 days determine G_E/G_M at Q² = 1.45 GeV² to $\pm$ 0.02, at 3.20 GeV² to $\pm$ 0.05 and at 4.90 GeV² to $\pm$ 0.10.