Generalized parton distributions from nucleon form factor data

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.

Nucleon electromagnetic form factors

“…In [Die05,Gui05], parameterizations of GPDs were developed which have a Regge behavior at small x and Q 2 , and which were modified to larger Q 2 behavior so as to lead to the observed power behavior of the FFs [Bur03,Bur04]. A modified Regge parameterization for H and E was proposed in [Gui05] :…”

“…Diehl et al [Die05] chose a more general functional form for E q at the expense of more free parameters. In the following, we discuss the 'minimal' model with 3 parameters, and refer the interested reader to [Die05] for a study of more general functional forms. The 3 free parameters in the resulting modified Regge ansatz are to be determined from a fit to the FF data.…”

Duality, analyticity, andtdependence of generalized parton distributions

“…In two recent papers [14,15] various forms of GPD for ξ = 0 were tested against the experimental data on the related form factors. The agreement with the data in Ref.…”

“…The effects are very large. Similarly to papers [14,15], we limit ourselves the case of vanishing skewedness, ξ = 0.…”

“…In the first approximation, the GPD is proportional to the imaginary part of a DVCS amplitude, therefore, as discussed in [10], the knowledge (or experimental reconstruction) of the DVCS amplitude may partly resolve the problem, provided the phase of the DVCS amplitude is also known. In other words, a GPD can be viewed as the imaginary part of an antiquark-nucleon scattering amplitude, or a quark-nucleon amplitude in the u channel.Alternatively, one can extract [11,12], still in a model-dependent way, the nontrivial interplay between the x and t dependence of GPD from light-cone wave functionswhere ψ(x, k ⊥ ) is a 2-particle wave function (see, e.g., [13]) and t ≡ q ⊥ .In two recent papers [14,15] various forms of GPD for ξ = 0 were tested against the experimental data on the related form factors. The agreement with the data in Ref.…”