Measurement of the Pion Form Factor

Cross sections for the electroproduction reaction $e+p\to e+n+{\pi }^{+}$ have been measured at invariant momentum transfers $k^2=-1, -3, -6\mathrm{}{\mathrm{F}}^{-2\mathrm{}}$. The circulating beam of the Cornell 2-GeV electron synchrotron struck a liquid-hydrogen target mounted in the synchrotron vacuum chamber in a field-free section between ring magnets. Pions produced along the momentum-transfer direction were counted in coincidence with in-elastically scattered electrons. Both were momentum analyzed by quadrupole magnets and detected in scintillation counters and (for the electrons) a shower Čerenkov counter. The effective mass of the final pion-nucleon system was varied from 1175 to 1300 MeV. The relative contribution of transverse and longitudinal photon exchanges was varied by changing the electron scattering angle. Electroproduction yields were normalized to elastic cross sections measured with the same electron spectrometer at the same incident energy. The eight measured cross sections have been compared with recent dispersion calculations. The agreement is very sensitive to the value chosen for the pion charge form factor, the only free parameter in the theory. Taking into account both experimental errors (typically 10% in the cross sections) and estimates of the reliability of the theory (also around 10%) based on comparison with other experiments, the following results were obtained: $F_{\pi }(-1\mathrm{} {\mathrm{F}}^{-2\mathrm{}})={{0.79}_{-0.18\mathrm{}}}^{+0.16\mathrm{}}$, $F_{\pi }(-3\mathrm{} {\mathrm{F}}^{-2\mathrm{}})=0.82\mathrm{}\pm 0.06$, and $F_{\pi }(-6\mathrm{} {\mathrm{F}}^{-2\mathrm{}})={{0.57}_{-0.09\mathrm{}}}^{+0.08\mathrm{}}$. Within the errors, the pion and proton charge form factors are idential. The pion form factor is also reasonably consistent with the $\rho$-exchange model: $F_{\pi }={\left(\frac{1-k^2}{m^2}\right)}^{-1\mathrm{}}$ with $m=600\mathrm{}\pm 80$ MeV. The root-mean-square charge radius of the pion is $r_{\pi }=\frac{\left(\sqrt{6}\right)}{m}=0.80\mathrm{}\pm 0.10$ F.