The high energy asymptotics of scattering processes in QCD

High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process, and thus to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate in particular the validity of the mean field approximation and how it is broken by fluctuations. We find that the mean field approximation is a good approximation in the initial stages of the evolution in rapidity.Comment: 31 pages, 20 figures. The code for BK evolution can be downloaded from http://www.isv.uu.se/~enberg/BK/ v2: several points clarified, discussion of the solutions to the mean-field evolution enhanced through the study of a different class of initial conditions, references added; conclusions unchanged. To appear in Phys. Rev.

Systematics of geometric scaling

Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A ``Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept \lambda. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.Comment: 4 pages, 4 figure

Hard diffraction and QCD multi-Pomeron vertices

We discuss the phenomenological and theoretical implications of recent progresses in the evaluation of multi-Pomeron vertices in high-energy perturbative QCD.Comment: Talk presented at DIS99, Zeuthen, April 19-23,199

QCD traveling waves at non-asymptotic energies

Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the ``interior'' of the wave front is obtained and compares well with numerical simulations of the original Balitsky-Kovchegov equation, even at non-asymptotic energies. Using this universal parametrization, we find evidence for a traveling-wave pattern of the dipole amplitude determined from the gluon distribution extracted from deep inelastic scattering data.Comment: 10 pages, 5 figures, minor revision, version to appear in PL

Hard diffraction at HERA in the dipole model of BFKL dynamics

Using the QCD dipole picture of the hard BFKL pomeron, we derive the general expressions of the elastic and inelastic components of the proton diffractive structure functions. We obtain a good 7 parameter fit (including a secondary reggeon contribution) to data taken at HERA by the H1 and ZEUS collaborations. The main characteristic features of the model in reproducing the data are discussed, namely the effective pomeron intercept, the scaling violations and the beta dependence. A difference obtained in the separate H1 and ZEUS fits leads us to analyse directly the differences between both measurements. Predictions on R, the ratio of longitudinal to transverse photon cross sections are performed and lead to very large values at high beta and large virtuality Q which may lead to a discrimination between models.Comment: uuencoded (latex file + 11 eps.figures), 27 page

On the QCD dipole content of hard photon and gluon probes

A gluon forward jet playing the role of a deep probe in high energy scattering, we analyze its infinite momentum QCD wave function in terms of dipole (color-singlet quark-antiquark) configurations using k_T-factorization properties. The comparison is made with virtual photon quark-antiquark configurations. Some implications for hard processes with forward jets at Hera and Tevatron are suggested.Comment: Invited talk at the QCD Euroconference 99,Montpellier July 7-13, 1999; 5pages, 1 eps figur

Universality and tree structure of high energy QCD

Using non-trivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitsky-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high energy scattering, in which a scattering process corresponds to a tree structure probed by a given source.Comment: 4 pages, 3 figure

Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff. We show that the Brunet-Derrida formula corresponds to the leading order expansion in the cut-off parameter of both the upper and lower bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula lies outside the allowed band determined from the bounds. If nonlinearities are neglected the upper and lower bounds coincide and are the exact linear speed for all values of the cut-off parameter.Comment: 8 pages, 3 figure