24 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
ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
The one loop vertex in QED is calculated in arbitrary covariant gauges as an
analytic function of its momenta. The vertex is decomposed into a longitudinal
part, that is fully responsible for ensuring the Ward and Ward-Takahashi
identities are satisfied, and a transverse part. The transverse part is
decomposed into 8 independent components each being separately free of
kinematic singularities in covariant gauge in a basis that modifies
that proposed by Ball and Chiu. Analytic expressions for all 11 components of
the vertex are given explicitly in terms of elementary functions
and one Spence function. These results greatly simplify in particular kinematic
regimes.Comment: 35 pages, latex, 2 figures, Complete postscript file available from:
ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9506/dtp9406.p
Vacuum replicas in QCD
The properties of the vacuum are addressed in the two- and four-dimensional
quark models for QCD. It is demonstrated that the two-dimensional QCD ('t Hooft
model) possesses only one possible vacuum state - the solution to the mass-gap
equation, which provides spontaneous breaking of the chiral symmetry (SBCS). On
the contrary, the four-dimensional theory with confinement modeled by the
linear potential supplied by the Coulomb OGE interaction, not only has the
chirally-noninvariant ground vacuum state, but it possesses an excited vacuum
replica, which also exhibits SBCS and can realize as a metastable intermediate
state of hadronic systems. We discuss the influence of the latter on physical
observables as well as on the possibility to probe the vacuum background fields
in QCD.Comment: RevTeX4, 26 pages, 8 EPS figures, extended references, corrected some
typos, to appear in Phys.Rev.
Chiral Symmetry Breaking in Quenched Massive Strong-Coupling QED
We present results from a study of subtractive renormalization of the fermion
propagator Dyson-Schwinger equation (DSE) in massive strong-coupling quenched
QED. Results are compared for three different fermion-photon proper vertex
{\it Ans\"{a}tze\/}: bare , minimal Ball-Chiu, and
Curtis-Pennington. The procedure is straightforward to implement and
numerically stable. This is the first study in which this technique is used and
it should prove useful in future DSE studies, whenever renormalization is
required in numerical work.Comment: REVTEX 3.0, 15 pages plus 7 uuencoded PostScript figure
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
Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
Toy models of interacting Pomerons with triple and quaternary Pomeron
vertices in zero transverse dimension are investigated. Numerical solutions for
eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained,
providing the quantum solution for the scattering amplitude in both models. The
equations of motion for the Lagrangians of the theories are also considered and
the classical solutions of the equations are found. Full two-point Green
functions ("effective" Pomeron propagator) and amplitude of diffractive
dissociation process are calculated in the framework of RFT-0 approach. The
importance of the loops contribution in the amplitude at different values of
the model parameters is discussed as well as the difference between the models
with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure
Renormalization and Chiral Symmetry Breaking in Quenched QED in Arbitrary Covariant Gauge
We extend a previous Landau-gauge study of subtractive renormalization of the
fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched
QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex
proposed by Curtis and Pennington with an additional correction term included
to compensate for the small gauge-dependence induced by the ultraviolet
regulator. We discuss the chiral limit and the onset of dynamical chiral
symmetry breaking in the presence of nonperturbative renormalization. We
extract the critical coupling in several different gauges and find evidence of
a small residual gauge-dependence in this quantity.Comment: REVTEX 3.0, 27 pages including 14 Extended Postscript files
comprising 9 figures. Replacement: discussion of chiral limit corrected, and
some minor typographical errors fixed. To appear in Phys. Rev.