Determination of the pion charge form factor for $Q^2=$ 0.60–1.60 GeV${}^2$

The data analysis for the reaction ${}^1\mathrm{H}$$(e,e^{\text{'}}{\pi }^{+})n$, which was used to determine values for the charged pion form factor $F_{\pi }$ for values of $Q^2=$ 0.6–1.6 GeV${}^2$, has been repeated with careful inspection of all steps and special attention to systematic uncertainties. Also the method used to extract $F_{\pi }$ from the measured longitudinal cross section was critically reconsidered. Final values for the separated longitudinal and transverse cross sections and the extracted values of $F_{\pi }$ are presented.

Figure 1

Representative missing mass distribution. Cuts at 0.925 and 0.960 GeV were applied to select the recoil neutron final state.

Figure 2

Example of the measured cross sections, $d^2\sigma /\mathit{dt}d\varphi$, as a function of ϕ at $Q^2=0.6$ GeV${}^2$ for two values of ε. The curves shown represent the model cross section used in the Monte Carlo simulation.

Figure 3

Separated cross sections ${\sigma }_L$ (solid) and ${\sigma }_T$ (open). The error bars represent the combination of statistical and $t$ uncorrelated systematic uncertainties. In addition, there is an overall systematic uncertainty of about 6%, mainly from the $t$ correlated, ε uncorrelated systematic uncertainty. The solid and dashed curves denote VGL model calculations for ${\sigma }_L$ and ${\sigma }_T$ with parameters ${\Lambda }_{\pi }^2=0.393$, 0.373, 0.412, 0.458 GeV${}^2$ for $Q^2=0.6\text{−}1.6$ GeV${}^2$, and with common ${\Lambda }_{\rho }^2=1.5$ GeV${}^2$. The discontinuities in the curves result from the different average $\overline{W}$ and ${\overline{Q}}^2$ of each $t$ bin.

Figure 4

Differential cross section comparison between our earlier $Q^2=0.75$ GeV${}^2$ results (open circles) (Ref. [13]) and this work (filled circles). The unseparated cross sections (${\sigma }_{\mathrm{uns}}=\epsilon {\sigma }_L+{\sigma }_T$) at high and low ε are nearly identical, but the differences between the separated ${\sigma }_L$ and ${\sigma }_T$ are somewhat larger. The ${\sigma }_{\mathrm{uns}}$ error bars include the statistical and epsilon uncorrelated systematics only and are in many cases smaller than the plotting symbols. Those for ${\sigma }_{L,T}$ include the contribution of all statistical and systematic uncertainties.

Figure 5

Values of ${\Lambda }_{\pi }^2$ determined from the fit of the VGL model to each $t$ bin, and linear fit to same. The error bars reflect the statistical and $t$-uncorrelated systematic uncertainties. The additional overall systematic uncertainties, which are applied after the fit, are not shown.

Figure 6

$Q^2{F}_{\pi }$ data from this work, compared to previously published data. The Brauel et al. [12] point has been reanalyzed using the $F_{\pi }$ extraction method of this work. The outer error bars for this work and the reanalyzed Brauel et al. data include all experimental and model uncertainties, added in quadrature, whereas the inner error bars reflect the experimental uncertainties only. Also shown are the light front quark model [6] (dash-dot), Dyson-Schwinger [7] (solid), QCD sum-rule [24] (dot), dispersion relation [25] (long-dash), and quark-hadron duality [26] (short-dash) calculations.