309 research outputs found
Reggeon Interactions in Perturbative QCD
We study the pairwise interaction of reggeized gluons and quarks in the Regge
limit of perturbative QCD. The interactions are represented as integral kernels
in the transverse momentum space and as operators in the impact parameter
space. We observe conformal symmetry and holomorphic factorization in all
cases.Comment: 13 pages LATEX, 2 figures using package FEYNMAN, N4-9
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
N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
We further investigate, in the planar limit of N=4 supersymmetric Yang Mills
theories,the high energy Regge behavior of six-point MHV scattering amplitudes.
In particular, for the new Regge cut contribution found in our previous paper,
we compute in the leading logarithmic approximation (LLA) the energy spectrum
of the BFKL equation in the color octet channel, and we calculate explicitly
the two loop corrections to the discontinuities of the amplitudes for the
transitions 2 to 4 and 3 to 3. We find an explicit solution of the BFKL
equation for the octet channel for arbitrary momentum transfers and investigate
the intercepts of the Regge singularities in this channel. As an important
result we find that the universal collinear and infrared singularities of the
BDS formula are not affected by this Regge-cut contribution. Any improvement of
the BDS formula should reproduce this cut to all orders in the coupling
Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
We investigate the Baxter equation for the Heisenberg spin model
corresponding to a generalized BFKL equation describing composite states of n
Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used
to find an unitary transformation from the impact parameter representation to
the representation in which the wave function factorizes as a product of Baxter
functions and a pseudo-vacuum state. We show that the solution of the Baxter
equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0,
1,...) and that the intercept for the composite Reggeon states is expressed
through the behavior of the Baxter function around the pole at lambda = i . The
absence of pole singularities in the two complex dimensional lambda-plane for
the bilinear combination of holomorphic and anti-holomorphic Baxter functions
leads to the quantization of the integrals of motion because the holomorphic
energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.
Regge Asymptotics of Scattering with Flavour Exchange in QCD
The contribution to the perturbative Regge asymptotics of the exchange of two
reggeized fermions with opposite helicity is investigated. The methods of
conformal symmetry known for the case of gluon exchange are extended to this
case where double-logarithmic contributions dominate the asymptotics. The Regge
trajectories at large momentum transfer are calculated.Comment: 18 pages LATEX, 3 figures using package FEYNMAN, N3-9
BFKL pomeron in the next-to-leading approximation
We find one-loop correction to the integral kernel of the BFKL equation for
the total cross section of the high energy scattering in QCD and calculate the
next-to-leading contribution to anomalous dimensions of twist-2 operators near
.Comment: 9 pages, LATEX, no figures, some comments correcte
Quasi-multi-Regge Processes with a Quark Exchange in the t-channel
The QCD amplitudes for particle's production in the quasi-multi-Regge
kinematics with a quark exchange in crossing channels are calculated in the
Born approximation. In particular they are needed to find next-to-leading
corrections to the quark Regge trajectory and to the integral kernel of the
Bethe-Salpeter equation for the t-channel partial wave with fermion quantum
numbers and a negative signature. The gauge-invariant action for the
interaction of the reggeized quarks and gluons with the usual particles is
constructed.Comment: LaTeX, 10 page
Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field
theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary
matrix which represents the single gluon scattering matrix. We discuss the
peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We
develop a perturbative expansion in the RFT framework, and find several
eigenstates of the zeroth order Hamiltonian. The zeroth order of this
perturbation preserves the number of - channel gluons. The eigenstates have
a natural interpretation in terms of the - channel exchanges. Studying the
single - channel gluon sector we find the eigenstates which include the
reggeized gluon and five other colored Reggeons. In the two ( - channel)
gluon sector we study only singlet color exchanges. We find five charge
conjugation even states. The bound state of two reggeized gluons is the
standard BFKL Pomeron. The intercepts of the other Pomerons in the large
limit are where is the intercept of the BFKL
Pomeron, but their coupling in perturbation theory is suppressed by at least
relative to the double BFKL Pomeron exchange. For the Pomeron
we find . We also find three charge
conjugation odd exchanges, one of which is the unit intercept
Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than
unity. We explain in what sense our calculation goes beyond the standard
BFKL/BKP calculation. We make additional comments and discuss open questions in
our approach.Comment: 58 pages, 4 figures, Extended version. To appear in JHE
Effective Action for High-Energy Scattering in Gravity
The multi-Regge effective action is derived directly from the linearized
gravity action. After excluding the redundant field components we separate the
fields into momentum modes and integrate over modes which correspond neither to
the kinematics of scattering nor to the one of exchanged particles. The
effective vertices of scattering and of particle production are obtained as
sums of the contributions from the triple and quartic interaction terms and the
fields in the effective action are defined in terms of the two physical
components of the metric fluctuation.Comment: 15 pages, LATE
Calculation of Reggeon Vertices in QCD
The method of calculation of effective vertices of interaction of the
Reggeized gluon and quark with particles in QCD in the next-to-leading order is
developed. The method is demonstrated in the case of already known vertices of
both gluon-gluon and quark-quark transitions in the scattering of gluons and
quarks on the Reggeized gluon. It is used for the calculation of the
gluon-quark transition in the scattering on the Reggeized quark.Comment: 27 pages, LaTex, 1 figure, uses axodraw.st
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