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Studying nuclear medium modification using the Gerasimov-Drell-Hearn sum rule

A. Deur, M. M. Dalton, S. Širca

TL;DR

This work shows that the Gerasimov–Drell–Hearn sum rule, when applied to nucleons embedded in nuclei, provides a powerful discriminant between uniform (mean-field) and non-uniform (SRC) medium modifications. By separating the GDH sum rule into a dynamic integral and a static part, the authors demonstrate that uniform modifications scale as $I^* = \chi^2 I$, while non-uniform SRC modifications follow a distinct, non-quadratic dependence, with further sensitivity to polarization effects such as D-wave depolarization. They propose practical strategies to extract the modified anomalous magnetic moment and mass, including combining the GDH and Schwinger sum rules and leveraging magnetic form-factor measurements, and discuss the connection to the EMC effect and the observability of global nucleon properties via sum rules. The work suggests that GDH measurements, complemented by additional observables, can illuminate the origin of medium modification in nuclei and potentially render global properties like $M^*$ and $\kappa^*$ observable in a model-independent way, with implications for understanding the EMC effect and the structure of bound nucleons.

Abstract

The Gerasimov-Drell-Hearn sum rule is a generic relation that has been used to make significant contributions to research in hadronic physics. It connects the spin-dependent cross-section for photoproduction off a particle to the squared ratio of the particle's anomalous magnetic moment and its mass, $(κ/M)^2$. Thus, for a nucleon embedded in a nucleus, the sum rule relates the cross-section to $κ/M$ averaged quadratically over the nucleons comprising the nucleus. This quadratic averaging can be used to constrain the mechanism responsible for the medium modification of the nucleon. We also point out that the global properties of the embedded nucleon like its axial charge, mass or magnetic moment are observables measurable through sum rules.

Studying nuclear medium modification using the Gerasimov-Drell-Hearn sum rule

TL;DR

This work shows that the Gerasimov–Drell–Hearn sum rule, when applied to nucleons embedded in nuclei, provides a powerful discriminant between uniform (mean-field) and non-uniform (SRC) medium modifications. By separating the GDH sum rule into a dynamic integral and a static part, the authors demonstrate that uniform modifications scale as , while non-uniform SRC modifications follow a distinct, non-quadratic dependence, with further sensitivity to polarization effects such as D-wave depolarization. They propose practical strategies to extract the modified anomalous magnetic moment and mass, including combining the GDH and Schwinger sum rules and leveraging magnetic form-factor measurements, and discuss the connection to the EMC effect and the observability of global nucleon properties via sum rules. The work suggests that GDH measurements, complemented by additional observables, can illuminate the origin of medium modification in nuclei and potentially render global properties like and observable in a model-independent way, with implications for understanding the EMC effect and the structure of bound nucleons.

Abstract

The Gerasimov-Drell-Hearn sum rule is a generic relation that has been used to make significant contributions to research in hadronic physics. It connects the spin-dependent cross-section for photoproduction off a particle to the squared ratio of the particle's anomalous magnetic moment and its mass, . Thus, for a nucleon embedded in a nucleus, the sum rule relates the cross-section to averaged quadratically over the nucleons comprising the nucleus. This quadratic averaging can be used to constrain the mechanism responsible for the medium modification of the nucleon. We also point out that the global properties of the embedded nucleon like its axial charge, mass or magnetic moment are observables measurable through sum rules.
Paper Structure (12 sections, 23 equations, 1 figure)

This paper contains 12 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Gerasimov--Drell--Hearn sum rule
  3. Medium modification of the sum rule
  4. Variation in GDH expectations for different medium modification scenarios
  5. $Z$-dependence of the GDH sum rule for an embedded nucleon
  6. Determination of $\kappa^*$ and $M^*$
  7. Separation of $\kappa^*$ and $M^*$ using the GDH and Schwinger sum rules
  8. Determination of $\kappa^*$ from magnetic form-factor measurements
  9. Determinations of $M^*$
  10. Connection to the EMC effect
  11. Global properties of embedded nucleons as observables
  12. Conclusion

Figures (1)

  • Figure 1: Expected value of the medium-modified GDH sum, $I^*$, normalized to the free-nucleon case, $I$, as a function of $\chi$, the average nuclear modification of $\kappa/M$. The dependencies for light nuclei ($N\approx Z$) based on the MF, SRC and SRC-DWD scenarios are shown by green, blue and red curves, respectively. The specific values of $I^\ast/I$ at $\chi=1.16$ and $1.30$ are given next to each curve.