109 research outputs found
QCD Saturation Equations including Dipole-Dipole Correlation
We derive two coupled non-linear evolution equations corresponding to the
truncation of the Balitsky infinite hierarchy of saturation equations after
inclusion of dipole-dipole correlations, i.e. one step beyond the
Balitsky-Kovchegov (BK) equation. We exhibit an exact solution for maximal
correlation which still satisfies the same asymptotic geometric scaling as BK
but with the S-matrix going to 1/2 (instead of 0) in the full saturation
region.Comment: 4 pages, no figure. Comment, references and acknowledgment adde
Geometric scaling as traveling waves
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-
Piscounov (KPP) equation to the problem of high energy evolution of the QCD
amplitudes. We explain how the traveling wave solutions of this equation are
related to geometric scaling, a phenomenon observed in deep-inelastic
scattering experiments. Geometric scaling is for the first time shown to result
from an exact solution of nonlinear QCD evolution equations. Using general
results on the KPP equation, we compute the velocity of the wave front, which
gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde
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
Eigenmodes of Decay and Discrete Fragmentation Processes
Linear rate equations are used to describe the cascading decay of an initial
heavy cluster into fragments. This representation is based upon a triangular
matrix of transition rates. We expand the state vector of mass multiplicities,
which describes the process, into the biorthonormal basis of eigenmodes
provided by the triangular matrix. When the transition rates have a scaling
property in terms of mass ratios at binary fragmentation vertices, we obtain
solvable models with explicit mathematical properties for the eigenmodes. A
suitable continuous limit provides an interpolation between the solvable
models. It gives a general relationship between the decay products and the
elementary transition rates.Comment: 6 pages, plain TEX, 2 figures available from the author
Universality of traveling waves with QCD running coupling
``Geometric scaling'', i.e. the dependence of DIS cross-sections on the ratio
Q/Q_S, where Q_S(Y) is the rapidity-dependent \saturation scale, can be
theoretically obtained from universal ``traveling wave'' solutions of the
nonlinear Balitsky-Kovchegov (BK) QCD evolution equation at fixed coupling. We
examine the similar mean-field predictions beyond leading-logarithmic order,
including running QCD coupling.Comment: 4 pages, 3 figures,, Invited talk given at the DIS 2007 Conference,
Munich, Germany, April 2007; Change of titl
Exclusive vector meson production at HERA from QCD with saturation
Following recent predictions that the geometric scaling properties of deep
inelastic scattering data in inclusive gamma*-p collisions are expected also in
exclusive diffractive processes, we investigate the diffractive production of
vector mesons. Using analytic results in the framework of the BK equation at
non-zero momentum transfer, we extend to the non-forward amplitude a
QCD-inspired forward saturation model including charm, following the
theoretical predictions for the momentum transfer dependence of the saturation
scale. We obtain a good fit to the available HERA data and make predictions for
deeply virtual Compton scattering measurements.Comment: 10 pages, 5 figures, full analysis including the charm contribution
and J/PSI production. Conclusions confirme
QCD traveling waves beyond leading logarithms
We derive the asymptotic traveling-wave solutions of the nonlinear
1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in
momentum-space, with 1-loop running coupling constant and equipped with the
Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic
accuracy, conveniently regularized by different resummation schemes. Traveling
waves allow to define "universality classes" of asymptotic solutions, i.e.
independent of initial conditions and of the nonlinear damping. A dependence on
the resummation scheme remains, which is analyzed in terms of geometric scaling
properties.Comment: 10 pages, 5 figures; typos corrected, references updated, final
Phys.Rev. D versio
Consequences of strong fluctuations on high-energy QCD evolution
We investigate the behaviour of the QCD evolution towards high-energy, in the
diffusive approximation, in the limit where the fluctuation contribution is
large. Our solution for the equivalent stochastic Fisher equation predicts the
amplitude as well as the whole set of correlators in the strong noise limit.
The speed of the front and the diffusion coefficient are obtained. We analyse
the consequences on high-energy evolution in QCD.Comment: 5 pages, 1 figure, more detailed discussions added, version to appear
in Phys. Rev.
Factorial Moments of Continuous Order
The normalized factorial moments are continued to noninteger values of
the order , satisfying the condition that the statistical fluctuations
remain filtered out. That is, for Poisson distribution for all .
The continuation procedure is designed with phenomenology and data analysis in
mind. Examples are given to show how can be obtained for positive and
negative values of . With being continuous, multifractal analysis is
made possible for multiplicity distributions that arise from self-similar
dynamics. A step-by-step procedure of the method is summarized in the
conclusion.Comment: 15 pages + 9 figures (figures available upon request), Late
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