Duality, analyticity, andtdependence of generalized parton distributions

Abstract

Basing upon dual analytic models, we present arguments in favor of the parametrization of generalized parton distributions (GPD) in the form ∼ (x/g 0 ) (1−x)α(t) , whereα(t) = α(t) − α(0) is the nonlinear part of the Regge trajectory and g 0 is a parameter, g 0 > 1. For linear trajectories it reduces to earlier proposals. We compare the calculated moments of these GPD with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier-transforming the obtained GPD, we access the spatial distribution of protons in the transverse plane. The relation between dual amplitudes with Mandelstam analyticity and composite models in the infinite momentum frame is discussed, the integration variable in dual models being associated with the quark longitudinal momentum fraction x in the nucleon.⋆ e-mail address: jenk@bitp.kiev.ua IntroductionGeneralized parton distributions (GPD) [1,2,3] combine our knowledge about the onedimensional parton distribution in the longitudinal momentum with the impact-parameter, or transverse distribution of matter in a hadron or nucleus. It is an ambitious program to access the spatial distribution of partons in the transverse plane and thus to provide a 3-dimensional picture of the nucleon (nucleus) [4,5,6,7,8]. This program involves various approaches, including perturbative QCD, Regge poles, lattice calculations etc. (see Ref.[9] for reviews). The main problem is that, while the partonic subprocess can be calculated perturbatively, the calculation of GPDs require non-perturbative methods. GPDs enter in hard exclusive processes, such as deeply virtual Compton scattering (DVCS); however, they cannot be measured directly but instead appear in convolution integrals, that cannot be easily converted. Hence the strategy is to guess the GPD, based on various theoretical constraints, and then compare it with the data. 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. [14] is impressive; in Ref.[15] the spatial distribution of partons in the transverse plane was also calculated. We pursue the approach of Refs. [14,15] by bringing more arguments coming from duality in favor of the parametrization for H(x, t) used in [14] and exploring how analyticity...

Inclusive and exclusive dilepton photoproduction at high energies

“…This assumption, due to its simplicity, is widely used in the literature, although it contradicts the Regge-pole theory, as shown, e.g., in studies of DVCS or GPDs, as shown, e.g., in Refs. [15,16]. We believe that the distinct assumptions for the t dependence will introduce an uncertainty on the overall normalization as we are considering only t-integrated cross sections in current study.…”

Generalized parton distributions and description of electromagnetic and graviton form factors of nucleon

“…This ansatz reproduces the basic properties of F 1 and provides a good description of the ratio of F 1 to F 2 and, consequently, of the ratio of G E to G M . A similar approach was examined in [28] with GPDs form…”

Impact Parameter Model for GPD

“…This result would pave the roads from the experimental data related to the amplitudes of the processes γ * p → γp (deeply virtual Compton scattering (DVCS)) and hard meson exclusive production γ * p → Mp to the studies of hadron structure in the two-dimensional transverse space. For the first time position space aspects of parton model were studied in the paper [8].A common procedure of obtaining GPD dependence is to guess the form of H q (x, ξ, t) proceeding from the model assumptions, namely use of the general constraints based on form-factors, first principles, experience gained from highenergy scattering and experimental studies of DVCS [10,11,12,13,14,15,16]. However, since impact parameter representation provides a useful framework for implementing geometrical aspects as well as transparent account of the unitarity constraints, it can be used as a complementary way for the GPD's modelling.…”

“…A common procedure of obtaining GPD dependence is to guess the form of H q (x, ξ, t) proceeding from the model assumptions, namely use of the general constraints based on form-factors, first principles, experience gained from highenergy scattering and experimental studies of DVCS [10,11,12,13,14,15,16]. However, since impact parameter representation provides a useful framework for implementing geometrical aspects as well as transparent account of the unitarity constraints, it can be used as a complementary way for the GPD's modelling.…”