770 research outputs found
A zero-dimensional model for high-energy scattering in QCD
We investigate a zero-dimensional toy model originally introduced by Mueller
and Salam which mimics high-energy scattering in QCD in the presence of both
gluon saturation and gluon number fluctuations, and hence of Pomeron loops.
Unlike other toy models of the reaction-diffusion type, the model studied in
this paper is consistent with boost invariance and, related to that, it
exhibits a mechanism for particle saturation close to that of the JIMWLK
equation in QCD, namely the saturation of the emission rate due to high-density
effects. Within this model, we establish the dominant high-energy behaviour of
the S-matrix element for the scattering between a target obtained by
evolving one particle and a projectile made with exactly n particles.
Remarkably, we find that all such matrix elements approach the black disk limit
S=0 at high rapidity Y, with the same exponential law: ~ exp(-Y) for all
values of n. This is so because the S-matrix is dominated by rare target
configurations which involve only few particles. We also find that the bulk
distribution for a saturated system is of the Poisson type.Comment: 34 pages, 9 figures. Some explanations added on the frame-dependence
of the relevant configurations (new section 3.3
Duality and Pomeron effective theory for QCD at high energy and large N_c
We propose an effective theory which governs Pomeron dynamics in QCD at high
energy, in the leading logarithmic approximation, and in the limit where N_c,
the number of colors, is large. In spite of its remarkably simple structure,
this effective theory generates precisely the evolution equations for
scattering amplitudes that have been recently deduced from a more complete
microscopic analysis. It accounts for the BFKL evolution of the Pomerons
together with their interactions: dissociation (one Pomeron splitting into two)
and recombination (two Pomerons merging into one). It is constructed by
exploiting a duality principle relating the evolutions in the target and the
projectile, more precisely, splitting and merging processes, or fluctuations in
the dilute regime and saturation effects in the dense regime. The simplest
Pomeron loop calculated with the effective theory is free of both ultraviolet
or infrared singularities.Comment: 13 pages, 1 figur
Comparing different hard-thermal-loop approaches to quark number susceptibilities
We compare our previously proposed hard-thermal-loop (HTL) resummed
calculation of quark number susceptibilities using a self-consistent two-loop
approximation to the quark density with a recent calculation of the same
quantity at the one-loop level in a variant of HTL-screened perturbation
theory. Besides pointing out conceptual problems with the latter approach, we
show that it severely over-includes the leading-order interaction effects while
including none of the plasmon term which after all is the reason to construct
improved resummation schemes.Comment: 6 pages, 6 figures. Revised version to appear in Eur. J. Phys.
Thermodynamics of the high-temperature quark-gluon plasma
We review the various methods which have been employed recently to describe
the thermodynamics of the high temperature quark-gluon plasma using weak
coupling techniques, and we compare their results with those of most recent
lattice gauge calculations. Many of the difficulties encountered with
perturbation theory at finite temperature are in fact not specific to QCD but
are present in any field theory at finite temperature and will be discussed
first in the simple example of the scalar field theory. We discuss the merits
and limitations of various techniques which have been used to go beyond
perturbation theory in the soft sector, such as dimensional reduction, screened
perturbation theory or hard-thermal-loop perturbation theory, and Phi-derivable
approximations. In the last part of the review, we focus on the later, which
lead to a remarkably simple expression for the entropy of the quark-gluon
plasma. When complemented with further, physically motivated, approximations,
this approach reproduces accurately the entropy obtained from lattice gauge
calculations at temperatures above 2.5 T_c, where T_c is the deconfinement
temperature. This calculation thus provides also support to the physical
picture of the quark-gluon plasma as a gas of weakly interacting
quasiparticles.Comment: Review for "Quark-Gluon Plasma 3", eds. R.C. Hwa and X.-N. Wang,
World Scientific, Singapore. 63 pages, 21 figures. v2: minor corrections and
2 references adde
The thermodynamics of the quark-gluon plasma: Self-consistent resummations vs. lattice data
We discuss a recent approach for overcoming the poor convergence of the
perturbative expansion for the thermodynamic potential of QCD. This approach is
based on self-consistent approximations which allow for a gauge-invariant and
manifestly ultraviolet-finite resummation of the essential physics of the hard
thermal/dense loops. The results thus obtained are in good agreement with
available lattice data down to temperatures of about twice the critical
temperature. Calculations for a plasma with finite quark density (i.e., with a
non-zero chemical potential ) are no more difficult than at .Comment: 4 pages LaTeX2e, contribution to the proceedings of the 15th
International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM
2001), Long Island, New York, January 15 - 20, 200
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
Dense-Dilute Duality at work: dipoles of the target
We explore the properties of the QCD high energy evolution in the limit of a
dilute target. Using the recently established property of selfduality of the
evolution operator (hep-ph/0502119), we show how to properly define the target
gluon and dipole creation operators in terms of dual Wilson lines (dual eikonal
factors). We explain how to expand these operators in terms of the functional
derivatives of the color charge density, in the situation when they act on the
eikonal factors of the projectile partons. We explicitly calculate the
expansion of the high energy evolution operator to fourth order in the
functional derivatives. Our result is infrared and ultraviolet finite, but does
not coincide with the formula given in hep-ph/0501088. We resolve this
discrepancy by showing that the identification of the dipole creation and
annihilation operators used in hep-ph/0501088 is incomplete, and provide the
required corrections to these definitions. The use of the corrected operators
in the calculational framework of hep-ph/0501088 reproduces our result. We also
prove that there is no discrepancy between the expansion of the JIMWLK equation
and the dualization of the expansion of the weak field limit.Comment: 18 pages, Explanations added. Version to appear in PR
JIMWLK evolution in the Gaussian approximation
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy
evolution of the n-point functions of the Wilson lines (the QCD scattering
amplitudes in the eikonal approximation) admit a controlled mean field
approximation of the Gaussian type, for any value of the number of colors Nc.
This approximation is strictly correct in the weak scattering regime at
relatively large transverse momenta, where it reproduces the BFKL dynamics, and
in the strong scattering regime deeply at saturation, where it properly
describes the evolution of the scattering amplitudes towards the respective
black disk limits. The approximation scheme is fully specified by giving the
2-point function (the S-matrix for a color dipole), which in turn can be
related to the solution to the Balitsky-Kovchegov equation, including at finite
Nc. Any higher n-point function with n greater than or equal to 4 can be
computed in terms of the dipole S-matrix by solving a closed system of
evolution equations (a simplified version of the respective Balitsky-JIMWLK
equations) which are local in the transverse coordinates. For simple
configurations of the projectile in the transverse plane, our new results for
the 4-point and the 6-point functions coincide with the high-energy
extrapolations of the respective results in the McLerran-Venugopalan model. One
cornerstone of our construction is a symmetry property of the JIMWLK evolution,
that we notice here for the first time: the fact that, with increasing energy,
a hadron is expanding its longitudinal support symmetrically around the
light-cone. This corresponds to invariance under time reversal for the
scattering amplitudes.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to
appear in JHE
Pomeron loops in zero transverse dimensions
We analyze a toy model which has a structure similar to that of the recently
found QCD evolution equations, but without transverse dimensions. We develop
two different but equivalent methods in order to compute the leading-order and
next-to-leading order Pomeron loop diagrams. In addition to the leading-order
result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb},
we can also calculate the next-to-leading order contribution which provides the
correction. We interpret this result and discuss its
possible implications for the four-dimensional QCD evolution.Comment: 11 pages, 4 figure
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