The Schwinger-Dyson equation on Pomeron loop summation and renormalization

The solution to the Schwinger-Dyson equation that describes the summation over Pomeron loop diagrams is derived. The solution is a closed expression which splits into two parts. The first leads directly to the renormalization of the BFKL Pomeron, and the second contribution is equivalent to non interacting Pomerons with renormalized vertices. Thus a closed expression is derived for the sum over Pomeron loop diagrams in the perturbative QCD approach, which preserves unitarity.Comment: 18 pages, 8 Figure

Selection rules at the quark-antiquark vertex of the QCD Pomeron

We derive the full analytic expression for the QCD eikonal coupling of a quark-antiquark state to the exchanged gluon-gluon state in the BFKL formalism. The formula is valid for all conformal spin configurations of the quark-antiquark and gluon-gluon states. In particular, a new selection rule on conformal spins characterizes the non-dominant BFKL components with intercept below the Pomeron in the conformal-invariant framework.Comment: 12 pages, latex with tcilatex, no figur

Revisiting the phenomenology on the QCD color dipole picture

Using the QCD dipole picture of the hard BFKL Pomeron, we perform a 3 parameter fit analysis of the recent inclusive structure function experimental measurements at small-$x$ and intermediate $Q^2$. As a byproduct, the longitudinal structure function and the gluon distribution are predicted without further adjustments. The data description is quite reasonable, being timely a further study using resummed NLO BFKL kernels along the lines of recent theoretical developments.Comment: Contribution to the ``International Workshop on Diffraction in High-Energy Physics'' (DIFFRACTION 2004), Cala Gonone (Sardinia, Italy), 18-23 September 2004; 3 pages, LaTeX fil

On Certain Two Dimensional Integrals that Appear In Conformal Field Theory

In a first part, we generalize a theorem for an holomorphic $\times$ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear combination of holomorphic times holomorphic generalized hypergeometric functions. The specific case $p=3$ is relevant to determine the triple Pomeron vertex in QCD.Comment: latex txt.tex, 3 files, 39 pages [SPhT-T00/034], submitted to Comm. Math. Phy

Deep-Inelastic Onium Scattering

Using the colour dipole approach of the QCD perturbative (BFKL) Pomeron exchange in onium-onium scattering, we compute the cross section for small but hierarchically different onium sizes. A specific term dependent on the size-ratio is generated. In deep inelastic onium scattering it appears as a scaling violation contribution to the quark structure function near the BFKL singularity. We find that the extension of the formalism for deep inelastic onium scattering to the proton structure function provides a remarkably good 3-parameter fit to HERA data at small x with a simple physical interpretation in terms of the dipole formulation.Comment: 10 pages, 2 Postscript figure

γ∗γ∗\gamma^*\gamma^* total cross-section in the dipole picture of BFKL dynamics

The total $\gamma^*\gamma^*$ cross-section is derived in the Leading Order QCD dipole picture of BFKL dynamics, and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the $e^+e^-$ collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomenologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity for observing BFKL.Comment: 24 pages, 4 figure