From QCD-Based Descriptions to Direct Fits: A Unified Study of Nucleon Electromagnetic Form Factors

TL;DR

This work addresses the challenge of describing nucleon electromagnetic form factors across a broad spacelike momentum transfer by unifying three theoretical perspectives: vector-meson dominance (VMD) in the large-$N_c$ limit, and two Generalized Parton Distribution (GPD) based approaches (ER with MRST2002 PDFs and VS24 with KKA10 PDFs). The authors construct four grouped models by weighting VMD, VS24, and ER components, fit them to electron-nucleon scattering data, and extract the relative contributions across different $t$ regimes; they further derive stable analytic Padé parametrizations for four groups of form factors. Two neutron-specific phenomenological representations (Regge-inspired for $tF_1^n$ and Padé for $G_M^n$) are used to validate and constrain the fits. The resulting Padé representations satisfy both low-$t$ analyticity requirements and high-$|t|$ scaling, providing a practical, physically motivated framework for nucleon structure studies with controlled model dependence.

Abstract

We present a detailed study of the nucleon electromagnetic form factors in the spacelike region by combining three complementary approaches: two GPD-based contributions and a vector-meson exchange component. By fitting experimental data, we extract the optimal weights and shape parameters describing the proton and neutron form factors. Global Padé-based fits are then constructed for four distinct groups of form factors, starting from local Taylor expansions and yielding stable analytic parametrizations over the analyzed $t$ range. The combined framework provides an accurate and physically motivated description of nucleon structure within a controlled model-dependent setting across a wide range of momentum transfers.

Figures (6)

• Figure 1: The combined model of $tF_1^{p}$, $tF_2^{p}$, $G_E^{P}$, and $G_M^{p}$ (group 1) as a function of $-t$. The ER Ansatz Guidal:2004nd+MSRT2002 PDF Martin:2002dr, the VS24 Ansatz Vaziri:2024fud with new parameters+KKA10 PDF Khorramian:2009xz, and the VMD model Masjuan:2012sk are used. We fit Combined model to the nucleon form factors, whose numerical values were extracted from experimental data and reported by the authors in Ref. Qattan:2012zf.
• Figure 2: The combined model of $G_E^{p}$, $G_M^{p}$ and $G_M^{n}$ (group 2) as a function of $-t$. The ER Ansatz Guidal:2004nd+MSRT2002 PDFs Martin:2002dr, the VS24 Ansatz Vaziri:2024fud with new parameters+KKA10 PDF Khorramian:2009xz, and the VMD model Masjuan:2012sk are used. We fit Combined model to the nucleon form factors, whose numerical values were extracted from experimental data and reported by the authors in Ref. Qattan:2012zf (upward triangles).
• Figure 3: The combined model of $tF_2^{n}$ and $G_M^{n}$ (group 3) as a function of $-t$. The ER Ansatz Guidal:2004nd+MSRT2002 PDFs Martin:2002dr, the VS24 Ansatz Vaziri:2024fud with new parameters+KKA10 PDF Khorramian:2009xz, and the VMD model Masjuan:2012sk are used. We fit Combined model to the nucleon form factors, whose numerical values were extracted from experimental data and reported by the authors in Ref. Qattan:2012zf.
• Figure 4: The combined model of $tF_1^{n}$ and $G_E^{n}$ ((group 4)) as a function of $-t$. The ER Ansatz Guidal:2004nd+MRST2002 PDFs Martin:2002dr, the VS24 Ansatz Vaziri:2024fud with new parameters+ new PDF(Eq. \ref{['eq:newpdf']}), and the VMD model Masjuan:2012sk are used.We fit Combined model to the nucleon form factors, whose numerical values were extracted from experimental data and reported by the authors in Ref. Qattan:2012zf.
• Figure 5: Comparison of phenomenological fits with neutron form factor data: (a) Regge-inspired linear Collins:1977jyDonnachie:2002en fit for $tF_1^n$, (b) Padé Arrington:2007uxMasjuan:2012wyEscribano:2015nraEscribano:2015yup fit for $G_M^n$ using data from Ref. Qattan:2012zf.