[Paper Review] Low-Q scaling, duality, and the EMC effect

J Arrington, R Ent+3 more|arXiv (Cornell University)|Jul 11, 2003

Fault Detection and Control Systems4 citations

TL;DR

This study presents the first direct measurement of the nuclear dependence of the inclusive structure function in the resonance region (W² < 4 GeV²), demonstrating that nuclear effects in the resonance region are identical to those in deep inelastic scattering (DIS), confirming quark-hadron duality. It observes for the first time an $A$-dependent shift in the high-$x$ crossover point, with carbon showing a lower crossover $x$ value than iron or gold, providing critical constraints on models of the EMC effect related to binding and Fermi motion.

ABSTRACT

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.

Motivation & Objective

• To investigate whether nuclear modifications in the resonance region exhibit the same $A$-dependence as in deep inelastic scattering (DIS), challenging the assumption that resonance region data are not scalable.
• To test quark-hadron duality by comparing structure function scaling behavior in the resonance region with that in the DIS regime.
• To extract precise nuclear modifications to the structure function in the resonance region for light and heavy nuclei, particularly at large $x$.
• To constrain models of the EMC effect by isolating contributions from binding and Fermi motion from potential exotic nuclear medium effects.
• To extend the $x$ and $Q^2$ range of EMC effect measurements beyond previous data, especially into the large-$x$ regime where few data exist.

Proposed method

• Utilized high-precision electron scattering data from Hall C at Jefferson Lab, covering the resonance region ($W^2 < 4$ GeV²) and extending to large $x$ values.
• Extracted nuclear structure functions from inclusive lepton-nucleus scattering data on carbon, iron, and gold.
• Compared the extracted structure functions with free nucleon structure functions to determine EMC ratios and assess $A$-dependence.
• Applied perturbative QCD scaling and duality arguments to test whether resonance region data exhibit the same $Q^2$-independent behavior as DIS data.
• Used theoretical models (e.g., Gross and Liuti, Burov et al.) to interpret the $A$-dependence of the high-$x$ crossover point.
• Performed a quantitative comparison of the $x$-dependence of the EMC ratio across different nuclei to test universality and binding effects.

Experimental results

Research questions

• RQ1 Does the EMC effect in the resonance region exhibit the same $A$-dependence as in the deep inelastic scattering regime, supporting quark-hadron duality?
• RQ2 Is there an $A$-dependent shift in the high-$x$ crossover point between light and heavy nuclei, indicating a role for nuclear binding and Fermi motion?
• RQ3 Can the observed $A$-dependence in the high-$x$ region be explained by conventional nuclear effects such as binding and Fermi motion, or does it require new physics?
• RQ4 Do the resonance region data show the same perturbative QCD scaling behavior as DIS data, confirming duality?
• RQ5 Is the $x$-dependence of the EMC ratio universal across different nuclei, or does it vary with $A$ as suggested by some models?

Key findings

• The nuclear modifications to the structure function in the resonance region are identical to those measured in deep inelastic scattering, confirming quark-hadron duality across kinematic regimes.
• For the first time, an $A$-dependent shift in the high-$x$ crossover point was observed, with carbon showing a lower crossover $x$ value than iron or gold.
• The observed $A$-dependence of the high-$x$ behavior is inconsistent with a recent effective field theory model predicting universal $x$-dependence.
• The data indicate that conventional nuclear effects—binding and Fermi motion—play a significant role across the entire $x$ region, not just at large $x$, and must be well constrained before exotic effects can be isolated.
• The uncertainty in extracting the EMC effect at large $x$ due to higher-twist contributions is small, suggesting high-precision measurements at large $x$ are feasible with current beam energies.
• The results support the predictions of models such as Gross and Liuti (1992), which predict a lower crossover point in lighter nuclei, and Burov et al. (1999), which predict differences between $^3$He and $^4$He.