790 research outputs found
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
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