Scaling of the $F_2$ Structure Function in Nuclei and Quark Distributions at $x>1$

We present new data on electron scattering from a range of nuclei taken in Hall C at Jefferson Lab. For heavy nuclei, we observe a rapid falloff in the cross section for $x>1$, which is sensitive to short-range contributions to the nuclear wave function, and in deep inelastic scattering corresponds to probing extremely high momentum quarks. This result agrees with higher energy muon scattering measurements, but is in sharp contrast to neutrino scattering measurements which suggested a dramatic enhancement in the distribution of the “superfast” quarks probed at $x>1$. The falloff at $x>1$ is noticeably stronger in ${}^2\mathrm{H}$ and ${}^3\mathrm{He}$, but nearly identical for all heavier nuclei.

Figure 1

$F_2$ for the E02-019 carbon data ($2.3\lesssim Q^2\lesssim 9{\mathrm{GeV}}^2$) as a function of $x$ (top set of points) and $\xi$ (middle), and $F_2^{(0)}$ vs $\xi$ (bottom). In each case, the higher points correspond to the smaller scattering angles.

Figure 2

$F_2^{(0)}$ vs $Q^2$ for fixed $\xi$ value. For this work and BCDMS, the carbon data are shown, while the SLAC points are carbon pseudodata taken from measurements on deuterium. The solid curves are the global fit, the short horizontal red lines show the BCDMS $\xi =1.15$ upper limit, and the green crosses show the falloff between $\xi =0.75$ and 1.05 based on the CCFR iron data (see text for details).

Figure 3

The slope $s$ in $\exp (-s\xi )$ as a function of $Q^2$. The targets are offset in $Q^2$ for visibility. Open symbols for ${}^2\mathrm{H}$ and ${}^3\mathrm{He}$ at low $Q^2$ are cases where the kinematic limit for the nucleus ($x\approx A$) corresponds to $\xi \lesssim 1.25$.

Figure 4

The extracted scaling structure function per nucleon for all nuclei at $Q^2=2.79$ and $7.35{\mathrm{GeV}}^2$. The deuteron data are kinematically limited to $x<2$, corresponding to $\xi \lesssim 1.15$ for the low $Q^2$ setting.