Coincidence Electroproduction of Charged Pions and the Pion Form Factor

We report measurements of the electroproduction reaction $e^{-}+p\to e^{-}+{\pi }^{+}+n$ carried out at the Cambridge Electron Accelerator by observing the final electron and pion in coincidence. The apparatus consisted of two focusing magnetic spectrometers equipped with wire spark chambers for determining the trajectories of the particles and with Čerenkov counters for particle identification. Data were collected in three scans which varied in turn one of the three variables: the photon mass squared $k^2$, the virtual photon-hadron center-of-mass energy $W$, or the angle $\theta$ between the virtual photon and the electroproduced pion in the virtual-photon-hadron center-of-mass system. The $k^{ 2}$-scan central settings were $k^{ 2}=-0.18,-0.30,-0.40,-0.80\mathrm{}$, and -1.20 Ge${\mathrm{V}}^2$ for $W=2.15\mathrm{}$ GeV and $\theta =0^{\circ }$; the $W$-scan central settings were $W=1.85,2.05,2.15\mathrm{}$, and 2.50 GeV for $k^{ 2}=-0.30\mathrm{}$ Ge${\mathrm{V}}^2$ and $\theta =0^{\circ }$; the central settings for the $\theta$ scan were $\theta =0^{\circ },7^{\circ }$, and 15° for $\phi =0^{\circ }$ and 180° and for $k^{ 2}=-0.40\mathrm{}$ Ge${\mathrm{V}}^2$ and $W=2.15\mathrm{}$ GeV. The data are analyzed to determine the longitudinal-transverse interference term and are compared with the predictions of a dispersion-theory calculation by Berends. The dispersion-theory model is used to extract the pion electromagnetic form factor. The result is consistent with $F_{\pi }=F_1^V$, but a simple $\rho$-pole form factor cannot be ruled out.