A precise extraction of the proton recoil polarization in $^4$He($\vec e,e^{\prime} \vec p\,$)$^3$H

I will present final results from the experiment E03-104 at Jefferson Lab where the proton recoil polarization in the $^4$He($\vec e,e^{\prime} \vec p\,$)$^3$H reaction was measured with unprecedented precision at $Q^2$ values of 0.8 (GeV/$c$)$^2$ and 1.3 (GeV/$c$)$^2$. We extracted both the polarization-transfer coefficients and the induced polarization. The precise extraction of the latter was only possible after extensive work to minimize false asymmetries, and provides a measure of final-state interactions. The measured ratio of polarization-transfer coefficients differs from a fully relativistic calculation by Udias {\it et al.}. The inclusion of a medium modification of the proton form factors predicted by a quark-meson coupling model or a chiral quark-soliton model brings the calculation in agreement with the data. Our data are equally well described by the prediction of Schiavilla {\it et al.} which instead uses free proton form factors but incorporates meson-exchange current effects and strong charge-exchange final state interactions. Neither theoretical calculation offers a satisfactory description of our induced polarization results.