14 research outputs found
Algebraic models for the hierarchy structure of evolution equations at small x
We explore several models of QCD evolution equations simplified by
considering only the rapidity dependence of dipole scattering amplitudes, while
provisionally neglecting their dependence on transverse coordinates. Our main
focus is on the equations that include the processes of pomeron splittings. We
examine the algebraic structures of the governing equation hierarchies, as well
as the asymptotic behavior of their solutions in the large-rapidity limit.Comment: 12 pages, 5 figures; minor changes in the revised versio
Impact parameter dependent S-matrix for dipole-proton scattering from diffractive meson electroproduction
We extract the S-matrix element for dipole-proton scattering using the data
on diffractive electroproduction of vector mesons at HERA. By considering the
full t dependence of this process we are able to reliably unfold the profile of
the S-matrix for impact parameter values b>0.3 fm. We show that the results
depend only weakly on the choice of the form for the vector meson wave
function. We relate this result to the discussion about possible saturation
effects at HERA.Comment: 15 pages, 6 figure
Tunneling transition to the Pomeron regime
We point out that, in some models of small-x hard processes, the transition
to the Pomeron regime occurs through a sudden tunneling effect, rather than a
slow diffusion process. We explain the basis for such a feature and we
illustrate it for the BFKL equation with running coupling by gluon rapidity
versus scale correlation plots.Comment: 17 pages, 5 figures, mpeg animations available from
http://www.lpthe.jussieu.fr/~salam/tunneling/ . v2 includes additional
reference
Geometric Scaling in a Symmetric Saturation Model
We illustrate geometric scaling for the photon-proton cross section with a
very simple saturation model. We describe the proton structure function F2 at
small x in a wide kinematical range with an elementary functional form and a
small number of free parameters. We speculate that the symmetry between low and
high Q2 recently discovered in the data could be related to a well-known
symmetry of the two-gluon- exchange dipole-dipole cross section.Comment: 15 pages, 4 figure
Minimal Subtraction vs. Physical Factorisation Schemes in Small-x QCD
We investigate the relationship of ``physical'' parton densities defined by
kt-factorisation, to those in the minimal subtraction scheme, by comparing
their small-x behaviour. We first summarize recent results on the above scheme
change derived from the BFKL equation at NLx level, and we then propose a
simple extension to the renormalisation-group improved (RGI) equation. In this
way we are able the examine the difference between resummed gluon distributions
in the Q_0 and MSbar schemes and also to show MSbar scheme resummed results for
P_gg and approximate ones for P_qg. We find that, due to the stability of the
RGI approach, small-x resummation effects are not much affected by the
scheme-change in the gluon channel, while they are relatively more sensitive
for the quark-gluon mixing.Comment: 14 pages, 8 figure
Traveling wave fronts and the transition to saturation
We propose a general method to study the solutions to nonlinear QCD evolution
equations, based on a deep analogy with the physics of traveling waves. In
particular, we show that the transition to the saturation regime of high energy
QCD is identical to the formation of the front of a traveling wave. Within this
physical picture, we provide the expressions for the saturation scale and the
gluon density profile as a function of the total rapidity and the transverse
momentum. The application to the Balitsky-Kovchegov equation for both fixed and
running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde
Next-to-leading and resummed BFKL evolution with saturation boundary
We investigate the effects of the saturation boundary on small-x evolution at
the next-to-leading order accuracy and beyond. We demonstrate that the
instabilities of the next-to-leading order BFKL evolution are not cured by the
presence of the nonlinear saturation effects, and a resummation of the higher
order corrections is therefore needed for the nonlinear evolution. The
renormalization group improved resummed equation in the presence of the
saturation boundary is investigated, and the corresponding saturation scale is
extracted. A significant reduction of the saturation scale is found, and we
observe that the onset of the saturation corrections is delayed to higher
rapidities. This seems to be related to the characteristic feature of the
resummed splitting function which at moderately small values of x possesses a
minimum.Comment: 34 page
Non-linear QCD dynamics and exclusive production in collisions
The exclusive processes in electron-proton () interactions are an
important tool to investigate the QCD dynamics at high energies as they are in
general driven by the gluon content of proton which is strongly subject to
parton saturation effects. In this paper we compute the cross sections for the
exclusive vector meson production as well as the deeply virtual Compton
scattering (DVCS) relying on the color dipole approach and considering the
numerical solution of the Balitsky-Kovchegov equation including running
coupling corrections. We show that the small- evolution given by this
evolution equation is able to describe the DESY-HERA data and is relevant for
the physics of the exclusive observables in future electron-proton colliders
and in photoproduction processes to be measured in coherent interactions at the
LHC.Comment: 6 pages, 4 figure
Limiting fragmentation in hadron-hadron collisions at high energies
Limiting fragmentation in proton-proton, deuteron-nucleus and nucleus-nucleus
collisions is analyzed in the framework of the Balitsky-Kovchegov equation in
high energy QCD. Good agreement with experimental data is obtained for a wide
range of energies. Further detailed tests of limiting fragmentation at RHIC and
the LHC will provide insight into the evolution equations for high energy QCD.Comment: 28 pages, 10 figures (2 new figures, text slightly expanded, and some
additional references