Polarization transfer in the ${}^2\mathrm{H}$$(\overrightarrow{e},e^{\prime }\overrightarrow{p})n$ reaction up to $Q^2=1.61(\mathrm{GeV}/c){}^2$

The recoil proton polarization was measured in the ${}^2\mathrm{H}$$(\overrightarrow{e},e^{\prime }\overrightarrow{p})n$ reaction in Hall A of the Thomas Jefferson National Accelerator Facility. The electron kinematics were centered on the quasielastic peak ($x_{\mathit{Bj}}\approx 1$) and included three values of the squared four-momentum transfer, $Q^2=0.43,1.00$ and 1.61 (GeV/$c){}^2$. For $Q^2=0.43$ and 1.61 (GeV/$c){}^2$, the missing momentum, $p_m$, was centered at zero, whereas for $Q^2=1.00(\mathrm{GeV}/c){}^2$ two values of $p_m$ were chosen: 0 and $174\mathrm{MeV}/c$. At low $p_m$, the $Q^2$ dependence of the longitudinal polarization, $P_z^{\prime }$, is not well described by a state-of-the-art calculation. Further, at higher $p_m$, a 3.5σ discrepancy was observed in the transverse polarization, $P_x^{\prime }$. Understanding the origin of these discrepancies is important to confidently extract the neutron electric form factor from the analogous ${}^2\mathrm{H}$$(\overrightarrow{e},e^{\prime }\overrightarrow{n})p$ experiment.

Figure 1

Coordinate system used to define the polarization components. The $Z$ axis is along the momentum transfer $\overrightarrow{q}$, the $Y$ axis is in the direction of $\overrightarrow{e}\hspace{1em}\times \overrightarrow{e}\hspace{1em}{}^{\prime }$ (where $\overrightarrow{e}\hspace{1em}$ and $\overrightarrow{e}\hspace{1em}{}^{\prime }$ are the momenta of the incident and scattered electron, respectively) and the $X$ axis is in the electron-scattering plane completing the right-handed system. Here, $\overrightarrow{p}\hspace{1em}$ is the momentum of the recoiling proton and ${\overrightarrow{p}}_m\hspace{1em}$ is the missing momentum. The “out-of-plane” angle is the angle between the two depicted planes, the scattering plane and the hadronic plane.

Figure 2

The filled diamonds are $\mu G_E/G_M$ for this experiment. Data from other Jefferson Lab experiments are labeled as JLAB00 [12], JLAB01 [29], and JLAB03 [27]. Data from other laboratories are labeled as MIT-Bates [25] and Mainz [13]. The curve shows $\mu G_E/G_M$ for the Lomon GKex(02S) form factors [28].

Figure 3

The open circles are the MIT-Bates data [25] and the solid squares represent the data from the present experiment. The dot-dashed curves are for the plane-wave Born approximation (PWBA), the dotted curves are for the distorted-wave Born approximation (DWBA), the dashed curves include MEC and IC, and the solid curves are the full calculations that also include relativistic corrections (RC). The top two panels show $P_x^{\prime }$ and $P_z^{\prime }$, normalized to the PWIA calculation. The third panel shows $P_x^{\prime }/P_z^{\prime }$ compared to the same ratio calculated in PWIA. The bottom panel shows the double ratio, defined in the text.

Figure 4

The polarizations $P_x^{\prime },P_z^{\prime }$ and the ratio $P_x^{\prime }/P_z^{\prime }$ as a function of $p_m$ at $Q^2=1.00$ (GeV/$c){}^2$. The $p_m$ values shown correspond to cross-section weighted averages. The labeling of the theoretical curves is the same as for the previous figure. At low $p_m$ all curves except for the solid (DWBA + MEC + IC + RC) are essentially indistinguishable. For $P_z^{\prime }$ at high $p_m$ the dotted (DWBA) and dashed (DWBA + MEC + IC) curves are indistinguishable.