Low-Q scaling, duality, and the EMC effect

High energy lepton scattering has been the primary tool for mapping out the quark distributions of nucleons and nuclei. Data on the proton and deuteron have shown that there is a fundamental connection between the low and high energy regimes, referred to as quark-hadron duality. We present the results of similar studies to more carefully examine scaling, duality, and in particular the EMC effect in nuclei. We extract nuclear modifications to the structure function in the resonance region, and for the first time demonstrate that nuclear effects in the resonance region are identical to those measured in deep inelastic scattering. With the improved precision of the data at large $x$, we for the first time observe that the large-$x$ crossover point appears to occur at lower $x$ values in carbon than in iron or gold.

Figure 1

The $F_2$ structure function per nucleon vs ξ for hydrogen (top), deuterium (middle), and iron (bottom). For the hydrogen and deuterium data (0.8 $<Q^2<$ 3.3 GeV${}^2$), the elastic (quasielastic) data have been removed. For the iron data ($Q^2<$ 5.0 GeV${}^2$), a cut of $W^2>1.2$ GeV${}^2$ is applied to remove the quasielastic peak. The curves are the MRST [13] (solid) and NMC [14] (dashed) parametrizations of the structure functions at $Q^2=4$ GeV${}^2$, with a parametrization of the EMC effect [15] applied to produce the curve for iron.

Figure 2

$F_2$ structure function per nucleon vs $Q^2$ for deuterium at fixed values of ξ. Dashed lines show a logarithmic $Q^2$ dependence, with the value of $d\ln F_2/d\ln Q^2$ determined at each ξ value from SLAC data at high $Q^2$ (up to 20 GeV${}^2$). The solid lines denote $W^2=2.0$ and 4.0 GeV${}^2$. The combined statistical and systematic uncertainties are shown. The hollow symbols are data from SLAC [18], while the solid symbols are from Jefferson Lab [7].

Figure 3

Ratio of nuclear to deuterium cross section per nucleon, corrected for neutron excess. The solid circles are Jefferson lab data taken in the resonance region ($1.2<W^2<3.0$ GeV${}^2,Q^2\approx 4$ GeV${}^2$). The hollow diamonds are SLAC E139 data, the crosses are the SLAC E87 data, and the hollow squares are BCDMS data, all in the DIS region. The scale uncertainties for the SLAC (left) and JLab (right) data are shown in the figure. The curves show an updated version [27] of the calculations from Ref. 28.