Induced Polarization in $^4$He$(e,e' \vec p)^3$H

The transferred polarization in the $^4$He($\vec e,e^\prime \vec p\,$)$^3$H reaction at $Q^2$ values of 0.4, 0.5, 1.0, 1.6, and 2.6 GeV$^2$ have been measured to study possible medium modifications of the proton form factors. The measured ratio of polarization-transfer coefficients was described by the inclusion of in-medium proton form factors. This interpretation was recently challenged by a calculation by Schiavilla {\it et al} including, particularly, a spin-dependent charge exchange in the final-state interaction (FSI). The induced polarization of the recoiling proton in this reaction is a measure of FSI. Precise data on these are key to shed more light on this controversy. Even more, a precise knowledge of the induced polarization will allow improvement of the FSI treatment by providing additional experimental constraints to existing theoretical calculations. In our follow-up experiment E03-104 at JLab high statistics data were taken at a $Q^2$ of 0.8 GeV$^2$ and 1.3 GeV$^2$ on $^1$H and $^4$He targets. The extraction of the small induced polarization is complicated by the possible presence of instrumental asymmetries in the focal-plane polarimeter. The induced polarization in the elastic $^1$H$(e,e'\vec p)$ reaction is (in one-photon approximation) zero and provides crucial information about these false asymmetries. Our preliminary results indicate an induced polarization of about $-0.03$ and seem to be in reasonable agreement with the RDWIA calculation of Udias {\it et al}.