The paper presents the QCD description of the small $x$ behaviour of parton distribution functions in the leading twist of Wilson operator product expansion. The smooth transition between the cases of the soft and hard Pomerons is obtained. The results are in qualitative agreement with deep inelastic experimental data.
We have carried out a NLO analysis of the world data on polarized DIS in the MS/bare scheme. We have studied two models of the parametrizations of the input parton densities, the first due to Brodsky, Burkhardt and Schmidt (BBS) which gives a simultaneous parametrization for both the polarized and unpolarized densities and in which the counting rules are strictly imposed, the second in which the input polarized densities are written in terms of the unpolarized ones in the generic form Deltaq(x)=f(x)q(x) with f(x) some simple smooth function. In both cases a good fit to the polarized data is achieved. As expected the polarized data do not allow a precise determination of the polarized gluon density. Concerning the polarized sea-quark densities, these are fairly well determined in the BBS model because of the interplay of polarized and unpolarized data, whereas in the second model, where only the polarized data are relevant, the polarized sea-quark densities are largely undetermined.
We provide a formulation of generalised vector dominance (GVD) for low-x deep-inelastic scattering that explicitly incorporates the ${gamma}^{ast} to q{bar q}$ transition and a QCD-inspired ansatz for the $(q{bar q})p$ forward-scattering amplitude. The destructive interference originally introduced in off-diagonal GVD is recovered in the present formulation and traced back to the generic structure of two-gluon-exchange as incorporated into the notion of colour transparency. Asymptotically, the transverse photoabsorption cross section behaves as (ln Q^2)/Q^2, implying a logarithmic violation of scaling for F_2, while the longitudinal-to-transverse ratio decreases as 1/ln Q^2.
Using renormalization group techniques we have derived analytic formulae for the next-to-leading order heavy-quark coefficient functions in deep inelastic lepton hadron scattering. These formulae are only valid in the kinematic regime Q^2 >> m^2, where Q^2 and m^2 stand for the masses squared of the virtual photon and heavy quark respectively. Some of the applications of these asymptotic formulae will be discussed.
We critically examine the question of scaling of the Deep Inelastic Scattering process in the medium Bjorken x region on a scalar boson in the framework of the AdS/QCD correspondence. To get the right polarization structure of the forward electroproduction amplitude, we show that one needs to add (at least) the scalar to scalar and scalar to vector hadronic amplitudes. This illustrates how the partonic picture may emerge from a simple scenario based on the AdS/QCD correspondence, provided one allows the conformal dimension of the hadronic field to equal 1 and use the concept of hadron - parton duality .
We compute the next-to-next-to-leading order (NNLO) QCD corrections to event shape distributions and their mean values in deep inelastic lepton-nucleon scattering. The magnitude and shape of the corrections varies considerably between different variables. The corrections reduce the renormalization and factorization scale uncertainty of the predictions. Using a dispersive model to describe non-perturbative power corrections, we compare the NNLO QCD predictions with data from the H1 and ZEUS experiments. The newly derived corrections improve the theory description of the distributions and of their mean values.