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DIS scattering, Structure Function Measurements

As was shown in Fig. 1, the structure function measured in E89-008 shows scaling in the Nachtmann variable $\xi$. This scaling occurs even at large values of $\xi$, where the scattering is dominated by resonance or even quasielastic scattering. This can be understood in terms of local duality, which leads to scaling on average of the proton structure function, and which leads directly to scaling for the nuclear structure function (the necessary averaging coming from the Fermi motion of the nucleons). This can also be viewed in terms of a near complete cancellation of the large higher twist contributions in the resonance region. In retrospect, it is not surprising that the nuclear structure function shows $\xi$-scaling in the resonance region, given the quantitative success of local duality in the proton structure function. This duality is seen if one averages over the entire resonance region or even if one averages in the region of a single resonance. However, the duality breaks down if one looks only at a fixed $W^2$ value (i.e. the top or side of a prominent resonance). Thus, the scaling in nuclei should break down where the Fermi motion is insufficient to average the proton structure function over a sufficient region. This occurs in deuterium (Fig. 5), where there is still a clear peak corresponding to the $\Delta$ resonance at low $Q^2$, as well as for the quasielastic peak in both deuterium and, to a lesser extent, iron (Fig. 1). However, these scaling violations are not seen for $\xi > 1$, even though we are averaging over only the low energy loss side of the quasielastic peak, and one would expect the averaging to be insufficient to invoke duality to explain the scaling. Additional data at high $\xi$ and high $Q^2$ (especially for light nuclei, which provide less averaging) will allow a more careful examination of scaling in this region.

Figure 5: Structure function per nucleon for deuterium vs. the Nachtmann scaling variable from Jefferson Lab E89-008. The $Q^2$ values are given for Bjorken $x=1$. Errors shown are statistical only. The arrows indicate the position of the quasielastic peak ($x=1$) for each data set.

This extended scaling for nuclei also means that the nuclear structure function as measured in the DIS region is the same as the structure measured at lower values of $W^2$. This scaling may allow measurements of the quark distributions in nuclei at lower $W^2$ (or equivalently lower $Q^2$ for fixed $\xi$) than accessible if one requires $W^2 > 4$ GeV$^2$. This may allow us to examine the $\xi$-dependence of the structure function for large values of $\xi$. This was measured at extremely high $Q^2$ values ($\sim 100$ GeV$^2$) in $\mu-$C scattering [32] and $\nu$-Fe scattering [33]. Near $\xi=1$, these experiments obtained significantly different results. The neutrino experiment (CCFR) found $F_2^{Fe} \propto \exp{(-8.3\xi)}$, consistent with the presence of significant SRCs, and the existence of superfast quarks in the nucleus (quarks carrying a momentum greater than that of a nucleon). The muon experiment (BCDMS) found a much faster falloff $F_2^C \propto \exp{(-16.5\xi)}$, which does not indicate large SRC contributions. This dependence was measured for C, Fe, and Au targets by E89-008, and for all targets the dependence was in general agreement with the BCDMS measurement ( $F_2^A \propto \exp{(-16\xi)}$). However, there are non-negligible contributions from the quasielastic peak in the vicinity of $\xi=1$, and there is still some $Q^2$ variation to the structure function falloff at the largest $Q^2$ values from E89-008. With a 6 GeV beam, we can reach $Q^2$ values of 8 GeV$^2$ and higher for $\xi \ge 1$, where quasielastic scattering is only a small contribution to the total cross section. The QE contribution will be much smaller than in the previous experiment, so we expect that the scaling violations seen in the E89-008 data will be significantly smaller for 6 GeV running and that the extracted $\xi$-dependence to become independent (or at least nearly independent) of $Q^2$.