[Paper Review] Nucleon Form Factors in the Space- and Timelike Regions

H.‐W. Hammer|arXiv (Cornell University)|May 31, 2001

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper presents a dispersion-theory analysis of nucleon electromagnetic form factors across spacelike and timelike momentum transfers, integrating unitarity, perturbative QCD, and experimental constraints. It further combines relativistic chiral perturbation theory with dynamical vector mesons to extend the chiral expansion’s validity to Q² ≈ 0.4 GeV², achieving good agreement with data and dispersion results for all four form factors.

ABSTRACT

Dispersion relations provide a powerful tool to describe the electromagnetic form factors of the nucleon both in the spacelike and timelike regions with constraints from unitarity and perturbative QCD. We give a brief introduction into dispersion theory for nucleon form factors and present results from a recent form factor analysis. Particular emphasis is given to the form factors in the timelike region. Furthermore, some recent results for the spacelike form factors at low momentum transfer from a ChPT calculation by Kubis and Meissner are discussed.

Motivation & Objective

• To extend the description of nucleon electromagnetic form factors into the timelike region using dispersion theory, where experimental data are sparse.
• To improve the low-energy description of spacelike form factors using relativistic chiral perturbation theory (ChPT) with infrared regularization.
• To enhance the convergence and validity of the chiral expansion by including dynamical vector mesons (ρ, ω, φ) via resonance saturation.
• To achieve a unified, model-independent description of nucleon form factors across all momentum transfers, bridging dispersive and effective field theory approaches.

Proposed method

• Utilizes unsubtracted and once-subtracted dispersion relations to relate form factors to their spectral functions via analyticity and unitarity.
• Constructs spectral functions from intermediate states (e.g., 2π, 3π, 4π) with quantum numbers matching the electromagnetic current, constrained by G-parity and isospin symmetry.
• Applies relativistic ChPT with infrared regularization to compute form factors at low spacelike momentum transfer, improving over heavy baryon ChPT by resumming 1/M recoil corrections.
• Introduces dynamical vector mesons (ρ, ω, φ) as fields in the Lagrangian, with t-dependent propagators to resum higher-order chiral corrections.
• Splits low-energy constants into vector meson contributions and residual terms (L_i → L̃_i + ∑_V a_i^V / (m_V² - t)) to incorporate resonance saturation without introducing new unknowns.
• Compares results with world data and dispersion analyses to validate the extended chiral framework.

Experimental results

Research questions

• RQ1 How can dispersion theory be used to describe nucleon form factors in both spacelike and timelike regions with unitarity and QCD constraints?
• RQ2 To what extent does relativistic ChPT with infrared regularization improve the convergence of the chiral expansion for nucleon form factors compared to heavy baryon ChPT?
• RQ3 Can the inclusion of dynamical vector mesons in ChPT extend the validity of the chiral expansion to higher momentum transfers, particularly for dipole-like form factors?
• RQ4 Why do neutron form factors in the timelike region near the N-N̄ threshold show larger magnitudes than predicted by current dispersive models?
• RQ5 How can dispersive and chiral effective field theory approaches be combined to achieve a consistent, model-independent description of nucleon form factors?

Key findings

• The inclusion of dynamical vector mesons in relativistic ChPT significantly improves the description of dipole-like form factors (G_M^n, G_E^p, G_M^p), extending the validity of the chiral expansion to Q² ≈ 0.4 GeV².
• Relativistic ChPT with infrared regularization outperforms heavy baryon ChPT, especially at low Q², due to proper resummation of 1/M recoil corrections.
• The neutron electric form factor G_E^n in relativistic ChPT shows good agreement with both experimental data and dispersion analyses, even after inclusion of vector mesons.
• The dispersion-theory-based analysis of timelike form factors reveals that neutron form factors near the N-N̄ threshold are larger than predicted, indicating a gap in current theoretical descriptions.
• The combined approach of dispersion theory and ChPT with dynamical vector mesons provides a consistent and accurate description of all four nucleon form factors across the full momentum transfer range.
• The method allows for a model-independent description of nucleon structure that incorporates both low-energy chiral symmetry and high-energy QCD constraints.