Generalized parton distributions from nucleon form factor data

TL;DR

Diehl, Feldmann, Jakob, and Kroll develop a simple, empirically constrained parameterization of generalized parton distributions at zero skewness, tying x- and t-dependence to forward PDFs and fitting nucleon form-factor data to extract valence quark transverse distributions. The framework yields tomographic images of the nucleon, quantifies valence contributions to Ji's angular-momentum sum rule, and informs the handbag description of wide-angle Compton scattering, including an assessment of the t-range where this approach is reliable. They explore the interplay between Regge behavior at small x and the soft Feynman mechanism at large t, study polarized and helicity-flip GPDs, and provide detailed uncertainty analyses and flavor-dependent insights. The work highlights the potential and current limits of extracting GPDs from elastic form factors and outlines data and theory directions needed to extend to nonzero skewness and sea-quark/gluon dynamics.

Abstract

We present a simple empirical parameterization of the x- and t-dependence of generalized parton distributions at zero skewness, using forward parton distributions as input. A fit to experimental data for the Dirac, Pauli and axial form factors of the nucleon allows us to discuss quantitatively the interplay between longitudinal and transverse partonic degrees of freedom in the nucleon ("nucleon tomography"). In particular we obtain the transverse distribution of valence quarks at given momentum fraction x. We calculate various moments of the distributions, including the form factors that appear in the handbag approximation to wide-angle Compton scattering. This allows us to estimate the minimal momentum transfer required for reliable predictions in that approach to be around |t|~3 GeV^2. We also evaluate the valence contributions to the energy-momentum form factors entering Ji's sum rule.

Figures (36)

• Figure 1: A three-quark configuration in the mixed representation of definite transverse position and definite plus-momentum. $x$ denotes the plus-momentum fraction of the upper quark with respect to the nucleon. The dashed line indicates the center of momentum of the two lower quarks and the thick solid line the center of momentum of the proton.
• Figure 2: Region of $x$ (white region) which accounts for $90\%$ of $F_1^p(t)$ in the best fit to (\ref{['fit:var1']}) at $\mu=2\,{\rm GeV}$. The upper and lower shaded $x$-regions each account for $5\%$ of $F_1^p(t)$, see (\ref{['eq:xminmax']}). The thick line shows the average $\langle x\rangle_t$ defined in (\ref{['eq:xavg']}).
• Figure 3: The function $l_q(x)$ from (\ref{['l-def']}) for the best fit to (\ref{['fit:var1']}) with $\mu=2\,{\rm GeV}$. The contributions from terms going with $\alpha'$ (dashed line) and $A_q$ (dotted line) are shown separately.
• Figure 4: The function $l_q(x)$ from (\ref{['l-def']}) for the best fit to (\ref{['fit:n2']}) with $\mu=2\,{\rm GeV}$. The contributions from terms going with $\alpha'$, $B_q$ and $A_q$ are shown separately.
• Figure 5: The distance $d_q(x)$ between struck quark and spectators, evaluated for the best fits to (\ref{['fit:n1']}) (dashed line) and (\ref{['fit:n2']}) (solid line) with $\mu=2\,{\rm GeV}$. The smallest $x$ value plotted is $5 \cdot 10^{-3}$. Shaded bands indicate the $1\, \sigma$ uncertainties of the fits as explained in App. \ref{['app:B']}.