170 research outputs found
A proof of the reggeized form of amplitudes with quark exchanges
A complete proof of the quark Reggeization hypothesis in the leading
logarithmic approximation for any quark--gluon inelastic process in the
multi--Regge kinematics in all orders of is given. First, we show
that the multi--Regge form of QCD amplitudes is guarantied if a set of
conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we
examine these conditions and show that they are satisfied.Comment: 22 pages, 7 figures, use elsart.cl
NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
We study next-to-leading corrections to the integral kernel of the BFKL
equation for high energy cross-sections in QCD and in supersymmetric gauge
theories. The eigenvalue of the BFKL kernel is calculated in an analytic form
as a function of the anomalous dimension \gamma of the local gauge-invariant
operators and their conformal spin n. For the case of an extended N=4 SUSY the
kernel is significantly simplified. In particular, the terms non-analytic in n
are canceled. We discuss the relation between the DGLAP and BFKL equations in
the N=4 model.Comment: Latex, 26 pages, typos corrected, to be published in Nucl.Phys.
Nonforward anomalous dimensions of Wilson operators in N=4 super-Yang-Mills theory
We present the next-to-leading order results for universal non-forward
anomalous dimensions of Wilson twist-2 operators in N=4 supersymmetric
Yang-Mills theory. The whole calculation was performed using supersymmetric
Ward identities derived in this paper together with already known QCD results
and does not involve any additional calculation of diagrams. We also considered
one particular limit of our result, which could potentially be interesting in
the context of AdS/CFT correspondence.Comment: 15 pages, references added, typos corrected, version accepted in JHE
Unintegrated gluon distributions in D* and dijet associated photoproduction at HERA
We consider the photoproduction of D* mesons associated with two hadron jets
at HERA collider in the framework of the kt-factorization approach. The
unintegrated gluon densities in a proton are obtained from the full CCFM, from
unified BFKL-DGLAP evolution equations as well as from the Kimber-Martin-Ryskin
prescription. Resolved photon contributions are reproduced by the initial-state
gluon radiation. We investigate different production rates and make comparison
with the recent experimental data taken by the ZEUS collaboration. Special
attention is put on the specific dijet correlations which can provide unique
information about non-collinear gluon evolution dynamics.Comment: 31 pages, 18 figure
Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
The multi--Regge form of QCD amplitudes with gluon exchanges is proved in the
next-to-leading approximation. The proof is based on the bootstrap relations,
which are required for the compatibility of this form with the s-channel
unitarity. We show that the fulfillment of all these relations ensures the
Reggeized form of energy dependent radiative corrections order by order in
perturbation theory. Then we prove that all these relations are fulfilled if
several bootstrap conditions on the Reggeon vertices and trajectory hold true.
Now all these conditions are checked and proved to be satisfied.Comment: 15 page
Exact resolution of the Baxter equation for reggeized gluon interactions
The interaction of reggeized gluons in multi-colour QCD is considered in the
Baxter-Sklyanin representation, where the wave function is expressed as a
product of Baxter functions Q(lambda) and a pseudo-vacuum state. We find n
solutions of the Baxter equation for a composite state of n gluons with poles
of rank r in the upper lambda semi-plane and of rank n-1-r in the lower lambda
semi-plane (0 leq r leq n-1). These solutions are related by n-2 linear
equations with coefficients depending on coth (pi lambda). The poles cancel in
the wave function, bilinear combination of holomorphic and anti-holomorphic
Baxter functions, guaranteeing its normalizability. The quantization of the
intercepts of the corresponding Regge singularities appears as a result of the
physical requirements that the holomorphic energies for all solutions of the
Baxter equation are the same and the total energies, calculated around two
singularities lambda, lambda^* --> + i or -i, coincide. It results in simple
properties of the zeroes of the Baxter functions. For illustration we calculate
the parameters of the reggeon states constructed from three and four gluons.
For the Odderon the ground state has conformal spin |m -m | = 1 and its
intercept equals unity. The ground state of four reggeized gluons possesses
conformal spin 2 and its intercept turns out to be higher than that for the
BFKL Pomeron. We calculate the anomalous dimensions of the corresponding
operators for arbitrary alpha_s/omega.Comment: LaTex, 42 pages, 8 .ps figures. Expanded and improved versio
Four loop reciprocity of twist two operators in N=4 SYM
The four loop universal anomalous dimension of twist-2 operators in N=4 SYM
has been recently conjectured. In this paper, we prove that it obeys a
generalized Gribov-Lipatov reciprocity, previously known to hold at the three
loop level.Comment: 15 pages, v3: Appendix A.3 added, main body shortened, version
accepted in JHE
Parton interactions in the Bjorken limit of QCD
We consider the Bjorken limit in the framework of the effective action
approach and discuss its similarities to the Regge limit. The proposed
effective action allows for a rather simple calculation of the known evolution
kernels. We represent the result in terms of two-parton interaction operators
involving gluon and quark operators depending on light-ray position and
helicity and analyze their symmetry properties.Comment: 32 pages LaTex, 4 eps-figures, comments added, minor correction
DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric
gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL
kernel in this model turns out to be an analytic function of the conformal spin
|n|. Its analytic continuation to negative |n| in the leading logarithmic
approximation allows us to obtain residues of anomalous dimensions \gamma of
twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation
in an agreement with their direct calculation from the DGLAP equation.
Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics
in the leading logarithmic approximation is integrable for an arbitrary number
of particles. In the next-to-leading approximation the holomorphic separability
of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter
kernel has the property of a hermitian separability. The main singularities of
anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations
in the next-to-leading approximation coincide but our accuracy is not enough to
verify an agreement for residues of subleading poles.Comment: 45 pages, latex. In the last version the expression (16) for the
t-channel partial wave of the process e+e- --> \mu+\mu- in the
double-logarithmic approximation at QED is corrected and its derivation is
given in the Appendix
Asymmetric Gluon Distributions and Hard Diffractive Electroproduction
The ``asymmetric'' matrix element that appears in the pQCD
description of hard diffractive electroproduction does not coincide with that
defining the gluon distribution function f_g(x). I outline a pQCD formalism
based on a concept of the double distribution F_g(x,y), which specifies the
fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum
transfer r, resp., carried by the gluons. For , r is
proportional to p: , and it is convenient to parameterize the
matrix element by an asymmetric distribution function depending on the total fractions and
of the initial hadron momentum p carried by the
gluons.I formulate evolution equations for , study some
of their general properties and discuss the relationship between , F_g(x,y) and f_g(x).Comment: Definition of asymmetric gluon distribution is corrected to conform
with the reduction formula
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