Proposed Kinematics with 6 GeV Beam

Fig. 10 shows the kinematic range in $x$ and $Q^2$. The region below the dashed (solid) curve is what is accessible with 4 (6) GeV beam at JLab ( $\theta \le 60^\circ$ in both cases). Experiment E89-008 did not cover the full $Q^2$ range for very large $x$ values, so the existing data for $x > 2.2$ is limited to $Q^2 \mathrel{\raise.3ex\hbox{$<$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}3.5$ GeV$^2$. Previous SLAC measurements of inclusive electron scattering from nuclei [1] were limited to $x\le 3$ and $Q^2\le 3~{\rm (GeV/c)}^2$. The same measured cross sections will then be examined as a function of the scaling variable $y$ and $Q^2$. Fig. 11 shows the kinematic range in $y$ and $Q^2$. Again, the dashed curve is what can be measured with 4 GeV beam, and the solid curve represents the coverage available with a 6 GeV beam. An addition to the measurement since the original proposal in 1994 is the inclusion of $^3$He and $^4$He cryogenic targets. The proposed data will significantly increase the $Q^2$ coverage for $^3$He and $^4$He compared to earlier SLAC measurements [42,1].

Figure 10: The kinematic range in $Q^2$ and the Bjorken $x$ variable. The region below the dashed curve is the range of data accessible with 4 GeV beam, and the region below the solid curve and indicates the range possible with a 6 GeV beam. The dotted line indicates the approximate $Q^2$ value where $\xi$-scaling is observed in the previous data. Experiment E89-008 did not cover the entire $Q^2$ range accessible at extremely large $x$ values ($x > 2$) so the current data for these large values of $x$ are limited to $\sim 3.5$ GeV$^2$ (just barely in the region where scaling is observed).

Figure 11: The kinematic range in $Q^2$ and the scaling variable $y$. The dashed curve indicates the coverage available with 4 GeV beam and the solid curve and the dashed curve indicates the increased range possible with a 6 GeV beam. The dotted line indicates the approximate $Q^2$ value where $y$-scaling is observed in the previous data.

The increase in beam energy to 6 GeV will have the greatest impact on the $Q^2$ range for kinematic points with $1.0 \mathrel{\raise.3ex\hbox{$<$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}x \mathrel{\raise.3ex\hbox{$<$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}1.7$. This extended $Q^2$ data is critical to studies of the transition from scattering from nucleons to scattering from quarks as described in the introduction. At larger values of $x$, the $Q^2$ increase is smaller, but is crucial for studies of the nature of the short range correlations. While the $Q^2$ increase is not as large as for the lower $x$ values, it is enough to allow us to reach well into the scaling region ( $Q^2 \mathrel{\raise.3ex\hbox{$>$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}3$ GeV$^2$) out to extremely large $x$ values. The 4 GeV measurement only reached $Q^2 \approx 3.5$ GeV$^2$ for $x > 2.2$, and while the $Q^2$ coverage for iron was much better for $1.5 < x < 2$, the deuterium data in this region was quite limited. The increased $Q^2$ range for large $x$ corresponds to a similar increase in $Q^2$ for large negative values of $y$ allowing direct study of the approach to the scaling limit, as well as data in the scaling region for extremely large values of $\vert y\vert$. This high $x$ (large negative $y$) region is very important in determining if the high momentum components are explained by two nucleon correlations or if large multinucleon correlations are required.

A beam energy of 6 GeV is sufficient to reach the scaling limit for the highest values of $x$ ($\approx 3$), and energies above 6 GeV do not significantly improve the $Q^2$ coverage for these very large values of $x$. Higher beam energies would have the most improvement in kinematic coverage for $x < 1.5$. However, the higher $Q^2$ values accessible in that $x$ region are not necessary for probing nucleon momentum distributions and short range correlations. One may be able to perform ``DIS'' experiments for $x \mathrel{\raise.3ex\hbox{$>$}\mkern-14mu \lower0.6ex\hbox{$\sim$}}1$ at extremely high $Q^2$ values (where the quasielastic and resonance contributions will disappear even for $x > 1$). Such an experiment would require energies well above 6 GeV. Thus, we feel that 6 GeV is the most appropriate energy for the proposed measurement.