Possibility for a New Measurement of the Proton Elastic Form Factor Ratio at Very Low $Q2$

The proton form factors at low $Q^2$ encode information about the peripheral structure of the proton as well as the interplay between the magnetic and electric charge distributions [1]. Furthermore, low $Q^2$ form factor measurements impact high precision experiments, for example, the measurement of the hydrogen hyperfine splitting [2]. Polarization transfer and beam target asymmetry measurements [3,4] allow determination of the electric to magnetic form factor ratio with unprecedented precision down to $Q^2 \simeq 0.15$ GeV$^2$. A new approved experiment at JLab will extend the $Q^2$ range down to 0.015 GeV$^2$. At even lower $Q^2$ the beam-target asymmetry method is impeded by the need to detect either a very forward electron or to use a low energy beam which must traverse the high magnetic field of a polarized target. We suggest an alternative measurement using colliding proton and electron beams which will allow a measurement of the form factor ratio to extremely low $Q^2$ ($\sim 10^{-4}$ GeV$^2$). The opportunity for this measurement will be discussed. \newline \textbf{References:} [1] G. A.~Miller, E.~Piasetzky and G.~Ron, Phys. Rev. Lett. {\bf 101}, 082002 (2008). [2] A. C. Zemach, Phys. Rev. {\bf 104}, 1771 (1956). [3] C.~B.~Crawford {\it et al.}, Phys. Rev. Lett. \textbf{98}, 052301 (2007). [4] G.~Ron {\it et al.}, Phys. Rev. Lett. {\bf 99}, 202002 (2007).