We argue that the t-dependence of the two-gluon form factor of the nucleon should be given by Γ(t) = (1 − t/m 2 2g ) −2 with m 2 2g ≈ 1GeV 2 . We demonstrate that this form provides a good description of the t-dependence of the cross section of the elastic photoproduction of J/ψ-mesons between the threshold region of E γ = 11 GeV (Cornell), E γ = 19 GeV (SLAC) and E γ = 100 GeV (FNAL) including the strong energy dependence of the t-slope. It is also well matched with the recent HERA data. The same assumption explains also the t-dependence of φ-meson electroproduction near threshold at W = 2.3 GeV, Q 2 = 1.0 GeV 2 .
Theoretical expectationsIt was demonstrated in [1] for the case of small x and in [2] in a general case that in the limit of large Q 2 the t-dependence of the process γ * L + N → V + N at fixed x is factorized into the convolution of a hard interaction block calculable in perturbative QCD, the short-distance qq wave function of the meson, and the generalized/skewed parton distribution (GPD) in the nucleon.In the scaling limit the t-dependence is originating solely from the GPD's since the meson wave function is highly squeezed in the direction transverse to the reaction axis. In the case of the valence quark exchanges these t-dependences are constrained by the sum rules for unpolarized [3] and polarized quarks [4] and could be also modeled in the chiral soliton models, see review in [5]. The t-dependence of GPD's provides unique information about the impact parameter distribution of the partons in nucleons. The knowledge of the transverse gluon distribution is especially important since it provides a key ingredient for the understanding of relative importance of soft and hard physics for high energy nucleonnucleon interactions at different impact parameters and has to be implemented in realistic Monte Carlo generators of nucleon-nucleon collisions at collider energies.In this paper we will first discuss theoretical expectations for the t-dependence of gluon GPD's. Next we will use the 11 ≤ E γ ≤ 100GeV data to check these expectations and hence 1