30 research outputs found
Universal features of JIMWLK and BK evolution at small x
In this paper we present the results of numerical studies of the JIMWLK and
BK equations with a particular emphasis on the universal scaling properties and
phase space structure involved. The results are valid for near zero impact
parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity
dependent saturation scale Q_s(\tau). Within the set of initial conditions
chosen both JIMWLK and BK equations show remarkable agreement. We point out the
crucial importance of running coupling corrections to obtain consistency in the
UV. Despite the scale breaking induced by the running coupling we find that
evolution drives correlators towards an asymptotic form with near scaling
properties. We discuss asymptotic features of the evolution, such as the \tau-
and A-dependence of Q_s away from the initial condition.Comment: 30 page
Running coupling and power corrections in nonlinear evolution at the high-energy limit.
A main feature of high-energy scattering in QCD is saturation in the number density of gluons.
This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have
been derived at leading logarithmic accuracy. In this paper we generalize this framework to
include running coupling corrections to the evolution kernel. We develop a dispersive representation
of the dressed gluon propagator in the background of Weiszšacker Williams fields and use
it to compute O(ÎČnâ1
0 αns
) corrections to the kernel to all orders in perturbation theory. The
resummed kernels present infrared-renormalon ambiguities, which are indicative of the form and
importance of non-perturbative power corrections. We investigate numerically the effect of the
newly computed perturbative corrections as well as the power corrections on the evolution and
find that at present energies they are both significant
Non-global jet evolution at finite N_c
Resummations of soft gluon emissions play an important role in many
applications of QCD, among them jet observables and small x saturation effects.
Banfi, Marchesini, and Smye have derived an evolution equation for non-global
jet observables that exhibits a remarkable analogy with the BK equation used in
the small x context. Here, this analogy is used to generalize the former beyond
the leading N_c approximation. The result shows striking analogy with the
JIMWLK equation describing the small x evolution of the color glass condensate.
A Langevin description allows numerical implementation and provides clues for
the formulation of closed forms for amplitudes at finite N_c. The proof of the
new equation is based on these amplitudes with ordered soft emission. It is
fully independent of the derivation of the JIMWLK equation and thus sheds new
light also on this topic.Comment: 22 page
Quark loop contribution to BFKL evolution: Running coupling and leading-N_f NLO intercept
We study the sea quark contribution to the BFKL kernel in the framework of
Mueller's dipole model using the results of our earlier calculation. We first
obtain the BFKL equation with the running coupling constant. We observe that
the ``triumvirate'' structure of the running coupling found previously for
non-linear evolution equations is preserved for the BFKL equation. In fact, we
rederive the equation conjectured by Levin and by Braun, albeit for the
unintegrated gluon distribution with a slightly unconventional normalization.
We obtain the leading-N_f contribution to the NLO BFKL kernel in transverse
momentum space and use it to calculate the leading-N_f contribution to the NLO
BFKL pomeron intercept for the unintegrated gluon distribution. Our result
agrees with the well-known results of Camici and Ciafaloni and of Fadin and
Lipatov. We show how to translate this intercept to the case of the quark
dipole scattering amplitude and find that it maps onto the expression found by
Balitsky.Comment: 27 pages; v2: some typos corrected, more discussion and references
added, the version to be published in Nucl. Phys.
Unitarity at small Bjorken x
This paper presents a solution to the nonlinear small x ``projectile side''
evolution equations as derived by Balitskii in 1996. The solution is based on
functional Fokker-Planck methods. The fixed point at small x is explicitly
calculated and all correlation functions in this limit are determined. They
show clear saturation and unitarization properties. Scaling laws that hold
during the saturation phase and throughout the whole course of the evolution
are established. The corresponding Langevin equations are given as a basis for
numerical simulations opening the field for future studies of dynamical issues
of the evolution not analytically accessible. The methods used may be extended
to the ``target side'' equations of Jalilian-Marian, Kovner, Leonidov and
Weigert.Comment: 28 pages, several diagrams. Typos corrected, minor useful changes in
notatio