Form factor ratio from unpolarized elastic electron-proton scattering

A reanalysis of unpolarized electron-proton elastic scattering data is done in terms of the electric to magnetic form factor squared ratio. This observable is in principle more robust against experimental correlations and global normalizations. The present analysis shows indeed that it is a useful quantity that contains reliable and coherent information. The comparison with the ratio extracted from the measurement of the longitudinal to transverse polarization of the recoil proton in polarized electron-proton scattering shows that the results are compatible within the experimental errors. Limits are set on the kinematics where the physical information on the form factors can be safely extracted. The results presented in this work bring a decisive piece of information to the controversy on the deviation of the proton form factors from the dipole dependence.

Figure 1

Correction factor as a function of $Q^2$. A linear fit (red line) shows an increasing of the factor. The dashed (blue) lines indicate that the extrapolated correction for the two HE points would be close to 1% rather than $\simeq 5\%$, as applied in the original paper.

Figure 2

${\mu }^2{R}^2={\mu }^2{(G_E/G_M)}^2$ as a function of $Q^2$ from Andivahis [51] as originally published, from analysis II without renormalization, and from analysis III omitting the lowest $\epsilon$ point, compared with the values from polarization experiments (GEp [17]).

Figure 3

${\mu }^2{R}^2={\mu }^2{(G_E/G_M)}^2$ as a function of $Q^2$ from Bartel [4], Christy [11], Janssens [53], and Berger [54] compared with the values from polarization experiments (GEp [17]).

Figure 4

Magnetic FF (normalized to $\mu$ and to the dipole) squared as a function of $Q^2$. Data are from Andivahis [51], Bartel [4], Christy [11], Janssens [53], Berger [54], Qattan [10], Walker [56], and Litt [9], compared with the calculation of Ref. [55], chosen as an example (black solid line).

Figure 5

Cross section normalized to the dipole cross section, $\sigma /{\sigma }_D$, as a function of $Q^2$ for different experiments: Andivahis [51], Qattan [10], Bartel [4], Christy [11], Litt [9], Walker [56], Janssens [53], Berger [54], Kirk [58].

Figure 6

Graphs representing data (open circles) from Ref. [51] and fits (red lines) of the reduced cross section as a function of $\epsilon$, at the $Q^2$ values reported at the top of each graph.

Figure 7

Same as Fig. 6, but for data from Ref. [53].

Figure 8

Same as Fig. 6, but for data from Ref. [4].

Figure 9

Same as Fig. 6, but for data from Ref. [54].

Figure 10

Same as Fig. 6 but for data from Ref. [11].

Figure 11

Same as Fig. 6, but for data from Ref. [56].

Figure 12

Same as Fig. 6, but for data from Ref. [9].

Figure 13

Same as Fig. 6, but for data from Ref. [10].