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

I will present final results on the extraction of the induced polarization P$_y$ in $^4$He($e,e^\prime \vec p\,$)$^3$H from experiment E03-104 at Jefferson Lab at $Q^2$ values of 0.8 (GeV/$c$)$^2$ and 1.3 (GeV/$c$)$^2$. False asymmetries complicate the extraction of P$_y$. Our experiment was uniquely set up to offer the same coverage in the proton acceptance in H($e,e^\prime \vec p\,$) as in $^4$He($e,e^\prime \vec p\,$)$^3$H and allow for a significant cancellation of false asymmetries in the difference. An extensive work was carried out to minimize false asymmetries. As a result we were able to reduce the experimental uncertainties in the difference of P$_y$ ($\Delta$P$_y$) extracted from $^4$He($e,e^\prime \vec p\,$)$^3$H and H($e,e^\prime \vec p\,$) by a factor of 3 compared to previous results. The greatly reduced experimental uncertainties result in an increased possible sensitivity of $\Delta$P$_y$ to higher order physics effects that yield a nonzero value for P$_y$ in H($e,e^\prime \vec p\,$) such as two-photon-exchange effects. We compare our results with two recent calculations for P$_y$, those of Udias {\it et al.} and Schiavilla {\it et al.}, which use different approaches to model final state interactions.