Linking Parton Distributions to Form Factors and Compton Scattering

TL;DR

Diehl, Feldmann, Jakob, and Kroll develop a framework connecting ordinary and skewed parton distributions to soft overlap contributions in elastic form factors and large‑angle Compton scattering using nucleon light‑cone wave functions in a multi‑Fock state expansion. They demonstrate that a simple valence‑plus‑few‑parton LCWF Ansatz reproduces unpolarised and polarised PDFs at large $x$, saturates the Dirac form factor $F_1(t)$ and the Compton amplitude with soft contributions, and yields Compton form factors $R_V(t)$ and $R_A(t)$ within the handbag approach. The work extends to higher Fock states to estimate soft overlap contributions beyond the valence sector and computes skewed parton distributions in the region $1>x>\,\zeta$, linking inclusive and exclusive observables in a process‑independent way. Overall, the results support soft overlap dominance in the kinematic range studied and provide a coherent scheme to connect DIS structure functions with exclusive reactions like form factors and Compton scattering, while offering concrete predictions for SPDs and Compton cross sections that can be tested experimentally.

Abstract

We relate ordinary and skewed parton distributions to soft overlap contributions to elastic form factors and large angle Compton scattering, using light-cone wave functions in a Fock state expansion of the nucleon. With a simple ansatz for the wave functions of the three lowest Fock states we achieve a good description of unpolarised and polarised parton distributions at large x, and of the data for the Dirac form factor and for Compton scattering, both of which can be saturated with soft contributions only. Large angle Compton scattering appears as a good case to investigate the relative importance of soft and hard contributions in exclusive processes which are sensitive to the end point regions of the nucleon wave function.

Figures (9)

• Figure 1: Overlap diagrams for (a) the elastic form factor and (b) Compton scattering. Lines $p$ and $p'$ denote protons, $k$ and $k'$ quarks or antiquarks, and the horizontal lines represent any number of spectator partons. The small blob attached to the photon lines stands for the pointlike quark-photon coupling in (a) and for the two diagrams of Fig. \ref{['handbagfig']} in (b).
• Figure 2: (a) $s$-channel and (b) $u$-channel diagram for quark-photon or antiquark-photon scattering.
• Figure 3: Parton distributions obtained from the $N=3,4,5$ Fock states ($P_3=0.17$, $P_4=P_5=0.1$). The model results are compared to the 1995 GRV LO parametrisation GRV at a factorisation scale of 1 GeV. For the sea distributions we sum over the three flavours.
• Figure 4: Spin-dependent valence quark distributions $\Delta {\rm u}_v$ and $\Delta {\rm d}_v$. The model results are compared to the parametrisation of Ref. glu96.
• Figure 5: Electromagnetic form factor of the proton and neutron using the model parton distributions for the valence Fock state only, the $N=3,4,5$ Fock states, and all Fock states on the basis of the GRV parametrisation at the factorisation scale 1 GeV GRV, cf. (\ref{['diseff']}). Data for $F_1$ and $G_M$ are taken from sil93lun93.