Nonforward parton densities and soft mechanism for form factors and wide-angle Compton scattering in QCD

TL;DR

The paper argues that at moderate momentum transfer |t| < 10 GeV^2, hadronic form factors and wide-angle Compton scattering are dominated by soft overlap mechanisms describable by nonforward parton densities (ND's) ${\cal F}(x;t)$. A simple Gaussian-based ND model, fixed by $F_1^p(t)$ data with $\lambda^2\approx 0.7$ GeV$^2$, reproduces the observed dipole-like $t$-dependence and magnitudes, and assigns the same ND's to wide-angle Compton scattering, predicting cross sections that agree in pattern with data though are systematically smaller by about a factor of two. The analysis argues that soft (handbag) contributions, rather than hard pQCD gluon exchanges, dominate in the accessible region, with double distributions providing the fundamental description and suggesting a path for more complete DD-based treatments and higher-precision measurements to refine the picture.

Abstract

We argue that at moderately large momentum transfer -t <10 GeV^2, hadronic form factors and wide-angle Compton scattering amplitudes are dominated by mechanism corresponding to overlap of soft wave functions. We show that the soft contribution in both cases can be described in terms of the same universal nonforward parton densities (ND's) F(x;t), which are the simplest hybrids of the usual parton densities and hadronic form factors. We propose a simple model for ND's possessing required reduction properties. Our model easily reproduces the observed magnitude and the dipole t-dependence of the proton form factor F_1^p(t) in the region 1 GeV^2 < -t < 10 GeV^2. Our results for the wide-angle Compton scattering cross section follow the angular dependence of existing data and are rather close to the data in magnitude.

Figures (10)

• Figure 1: $a)$ General Compton amplitude; $b)$$s$-channel handbag diagram; $c)$$u$-channel handbag diagram.
• Figure 2: $a)$ Structure of the effective two-body contribution to form factor in the light cone formalism. $b)$ Form factor as an $x$-integral of nonforward parton densities.
• Figure 3: Ratio $F_1^p(t)/D(t)$ of the $F_1^p(t)$ form factor to the dipole fit $D(t) =1/(1-t/0.71\,{\rm GeV^2})^2$. Curve is based on Eqs.(16)-(18) with $\lambda ^2 = 0.7 \, {\rm GeV}^2$. Experimental data are taken from ref.[18].
• Figure 4: Some configurations responsible for power-law asymptotic contributions for the WACS amplitude.
• Figure 5: Terms having $O(s^0)$ behavior for large $s$.