Measurement of Proton Electromagnetic Form Factors in $e^{+}{e}^{-}\to p\overline{p}$ in the Energy Region 2.00–3.08 GeV

The process of $e^{+}{e}^{-}\to p\overline{p}$ is studied at 22 center-of-mass energy points ($\sqrt{s}$) from 2.00 to 3.08 GeV, exploiting $688.5{\mathrm{pb}}^{-1}$ of data collected with the BESIII detector operating at the BEPCII collider. The Born cross section (${\sigma }_{p\overline{p}}$) of $e^{+}{e}^{-}\to p\overline{p}$ is measured with the energy-scan technique and it is found to be consistent with previously published data, but with much improved accuracy. In addition, the electromagnetic form-factor ratio ($|G_E/G_M|$) and the value of the effective ($|G_{\text{eff}}|$), electric ($|G_E|$), and magnetic ($|G_M|$) form factors are measured by studying the helicity angle of the proton at 16 center-of-mass energy points. $|G_E/G_M|$ and $|G_M|$ are determined with high accuracy, providing uncertainties comparable to data in the spacelike region, and $|G_E|$ is measured for the first time. We reach unprecedented accuracy, and precision results in the timelike region provide information to improve our understanding of the proton inner structure and to test theoretical models which depend on nonperturbative quantum chromodynamics.

Figure 1

Lowest-order Feynman diagrams for elastic electron-baryon scattering $e^{-}B\to e^{-}B$ (a), and for the annihilation process $e^{-}{e}^{+}\to B\overline{B}$ (b). $B$ is a baryon.

Figure 2

Fit to the $|\cos \theta |$ distributions at (a) 2.125 GeV and (b) 2.396 GeV after the application of angular-dependent $\epsilon (1+\delta )$ factors.

Figure 3

Results from this analysis (red solid squares) including statistical and systematic uncertainties for (a) the $e^{+}{e}^{-}\to p\overline{p}$ cross section and a fit through the data (blue solid line); (b) the ratio $|G_E/G_M|$ of the proton; (c) the electric FF of the proton $|G_E|$; (d) the magnetic FF of the proton $|G_M|$; (e) the effective FF of the proton $|G_{\text{eff}}|$ and a fit through the data (blue solid line) by Eq. (7) suggested in Ref. [16]; (f) Proton effective FF values, after subtraction of the smooth function described by Eq. (7), as a function of the relative momentum $p$. Also shown are previously published measurements from BESIII [8, 15], BABAR [14], CMD3 [10], BES [4], FENICE [9], E760 [12], E835 [13], PS170 [11], and DM2 [6]. ${\chi }^2={\sum }_i[f(x_i)-y_i{]}^2/{\mathrm{err}}_i^2$, where ${\mathrm{err}}_i$ is the error of the measured results including statistical and correlated systematic uncertainties, $f$ is the fit function, ndf is the number of degrees of freedom.