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The influence of Fermi motion on the comparison of the polarization transfer to a proton in elastic $vec ep$ and quasi-elastic $vec eA$ scattering

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 Added by Sebouh Paul
 Publication date 2019
  fields
and research's language is English




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A comparison between polarization-transfer to a bound proton in quasi-free kinematics by the A$(vec{e},evec p)$ knockout reaction and that in elastic scattering off a free proton can provide information on the characteristics of the bound proton. In the past the reported measurements have been compared to those of a free proton with zero initial momentum. We introduce, for the first time, expressions for the polarization-transfer components when the proton is initially in motion and compare them to the $^2$H data measured at the Mainz Microtron (MAMI). We show the ratios of the transverse ($P_x$) and longitudinal ($P_z$) components of the polarization transfer in $^2textrm{H}(vec{e},evec p)textrm{n}$, to those of elastic scattering off a moving proton, assuming the protons initial (Fermi) momentum equals the negative missing momentum in the measured reaction. We found that the correction due to the proton motion is up to 20% at high missing momentum. However the effect on the double ratio $frac{(P_x/P_z)^A}{(P_x/P_z)^{^1!textrm{H}}}$ is largely canceled out, as shown for both $^2$H and $^{12}$C data. This implies that the kinematics is not the primary cause for the deviations between quasi-elastic and elastic scattering reported previously.



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Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $G_{E}/G_{M}$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $H(vec{e},evec{p})$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2 = 2.5$ GeV$^2$, spanning a wide range of the virtual photon polarization parameter, $epsilon$. From these measured polarization observables, we have obtained separately the ratio $R$, which equals $mu_p G_{E}/G_{M}$ in the Born approximation, and the longitudinal polarization transfer component $P_ell$, with statistical and systematic uncertainties of $Delta R approx pm 0.01 mbox{(stat)} pm 0.013 mbox{(syst)}$ and $Delta P_ell/P^{Born}_{ell} approx pm 0.006 mbox{(stat)}pm 0.01 mbox{(syst)}$. The ratio $R$ is found to be independent of $epsilon$ at the 1.5% level, while the $epsilon$ dependence of $P_ell$ shows an enhancement of $(2.3 pm 0.6) %$ relative to the Born approximation at large $epsilon$.
We report the first precision measurement of the proton electric to magnetic form factor ratio from spin-dependent elastic scattering of longitudinally polarized electrons from a polarized hydrogen internal gas target. The measurement was performed at the MIT-Bates South Hall Ring over a range of four-momentum transfer squared $Q^2$ from 0.15 to 0.65 (GeV/c)$^2$. Significantly improved results on the proton electric and magnetic form factors are obtained in combination with previous cross-section data on elastic electron-proton scattering in the same $Q^2$ region.
The effects of multi-photon-exchange and other higher-order QED corrections on elastic electron-proton scattering have been a subject of high experimental and theoretical interest since the polarization transfer measurements of the proton electromagnetic form factor ratio $G_E^p/G_M^p$ at large momentum transfer $Q^2$ conclusively established the strong decrease of this ratio with $Q^2$ for $Q^2 gtrsim 1$ GeV$^2$. This result is incompatible with previous extractions of this quantity from cross section measurements using the Rosenbluth Separation technique. Much experimental attention has been focused on extracting the two-photon exchange (TPE) effect through the unpolarized $e^+p/e^-p$ cross section ratio, but polarization transfer in polarized elastic scattering can also reveal evidence of hard two-photon exchange. Furthermore, it has a different sensitivity to the generalized TPE form factors, meaning that measurements provide new information that cannot be gleaned from unpolarized scattering alone. Both $epsilon$-dependence of polarization transfer at fixed $Q^2$, and deviations between electron-proton and positron-proton scattering are key signatures of hard TPE. A polarized positron beam at Jefferson Lab would present a unique opportunity to make the first measurement of positron polarization transfer, and comparison with electron-scattering data would place valuable constraints on hard TPE. Here, we propose a measurement program in Hall A that combines the Super BigBite Spectrometer for measuring recoil proton polarization, with a non-magnetic calorimetric detector for triggering on elastically scattered positrons. Though the reduced beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of TPE.
We report the first measurements of the transverse ($P_{x}$ and $P_{y}$) and longitudinal ($P_{z}$) components of the polarization transfer to a bound proton in the deuteron via the $^{2}mathrm{H}(vec{e},evec{p})$ reaction, over a wide range of missing momentum. A precise determination of the electron beam polarization reduces the systematic uncertainties on the individual components, to a level that enables a detailed comparison to a state-of-the-art calculation of the deuteron that uses free-proton electromagnetic form factors. We observe very good agreement between the measured and the calculated $P_{x}/P_{z}$ ratios, but deviations of the individual components. Our results cannot be explained by medium modified electromagnetic form factors. They point to an incomplete description of the nuclear reaction mechanism in the calculation.
We present measurements of the electron helicity asymmetry in quasi-elastic proton knockout from $^{2}$H and $^{12}$C nuclei by polarized electrons. This asymmetry depends on the fifth structure function, is antisymmetric with respect to the scattering plane, and vanishes in the absence of final-state interactions, and thus it provides a sensitive tool for their study. Our kinematics cover the full range in off-coplanarity angle $phi_{pq}$, with a polar angle $theta_{pq}$ coverage up to about 8 degrees. The missing energy resolution enabled us to determine the asymmetries for knock-out resulting in different states of the residual $^{11}$B system. We find that the helicity asymmetry for $p$-shell knockout from $^{12}$C depends on the final state of the residual system and is relatively large (up to $approx 0.16$), especially at low missing momentum. It is considerably smaller (up to $approx 0.01$) for $s$-shell knockout from both $^{12}$C and $^2$H. The data for $^2$H are in very good agreement with theoretical calculations, while the predictions for $^{12}$C exhibit differences with respect to the data.
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