Dual analytic model of generalized parton distributions
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ELEMENTARY PARTICLES AND FIELDS Theory
Dual Analytic Model of Generalized Parton Distributions* L. L. Jenkovszky** Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine Received October 17, 2006; in final form, June 27, 2007 ˜ Abstract—A model for generalized parton distributions (GPDs) in the form of ∼(x/g0 )(1−x)α(t) , where α ˜ (t) = α(t) − α(0) is the nonlinear part of the Regge trajectory and g0 is a parameter, g0 > 1, is presented. For linear trajectories, it reduces to earlier proposals. We compare the calculated moments of these GPDs 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 GPDs, 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.
PACS numbers: 12.40.Nn, 12.38.Bx, 13.60.Hb DOI: 10.1134/S1063778808020166
1. INTRODUCTION An ambitious program to access the spatial distribution of partons in the transverse plane and thus to provide a three-dimensional picture of the nucleon (nucleus) has been recently put forward [1–5]. This program involves various approaches, including perturbative QCD, Regge poles, lattice calculations, etc. (see [6] for reviews). It is based on generalized parton distributions (GPDs) [7–9], which combine our knowledge about the one-dimensional parton distribution in the longitudinal momentum with the impact parameter, or transverse distribution of matter in a hadron or nucleus. The main problem is that, while the partonic subprocess can be calculated perturbatively, the calculation of GPDs requires nonperturbative 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, which cannot be easily converted. Hence, the strategy is to guess the GPDs, based on various theoretical constraints, and then compare them 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 ∗ **
The text was submitted by the authors in English. E-mail: [email protected]
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 lightcone wave functions: H(x, ξ = 0, t) =
d2 k⊥ ψ ∗ (x, k⊥ )ψ(x, k⊥ + (1 − x)q⊥ ),
where ψ(x, k⊥ ) is a two-particle wave function (see, e.g., [13]) and t ≡ |q⊥ |. In
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