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 $\ensuremath{\sim}(x/{g}_{0}{)}^{(1\ensuremath{-}x)\stackrel{\texttildelow{}}{\ensuremath{\alpha}}(t)}$, where $\stackrel{\texttildelow{}}{\ensuremath{\alpha}}(t)=\ensuremath{\alpha}(t)\ensuremath{-}\ensuremath{\alpha}(0)$ is the nonlinear part of the Regge trajectory and ${g}_{0}$ is a parameter. 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.