442 research outputs found
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
Mandelstam cuts and light-like Wilson loops in N=4 SUSY
We perform an analytic continuation of the two-loop remainder function for
the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin,
Vergu and Volovich from the light-like Wilson loop representation. The
remainder function is continued into a physical region, where all but two
energy invariants are negative. It turns out to be pure imaginary in the
multi-Regge kinematics, which is in an agreement with the predictions based on
the Steinmann relations for the Regge poles and Mandelstam cut contributions.
The leading term reproduces correctly the expression calculated by one of the
authors in the BFKL approach, while the subleading term presents a result, that
was not yet found with the use of the unitarity techniques. This supports the
applicability of the Wilson loop approach to the planar MHV amplitudes in N=4
SUSY.Comment: 11 pages, 4 figure
BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
After a brief review of the BFKL approach to Regge processes in QCD and in
supersymmetric (SUSY) gauge theories we propose a strategy for calculating the
next-to-next-to-leading order corrections to the BFKL kernel. They can be
obtained in terms of various cross-sections for Reggeized gluon interactions.
The corresponding amplitudes can be calculated in the framework of the
effective action for high energy scattering. In the case of N=4 SUSY it is also
possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the
analytic properties of the BDS amplitudes at high energies are investigated, in
order to verify their self-consistency. It is found that, for the number of
external particles being larger than five, these amplitudes, beyond one loop,
are not in agreement with the BFKL approach which predicts the existence of
Regge cuts in some physical channels.Comment: 41 pages, expanded version with many clarifications and new
references, conclusions unchanged. Note adde
Analytic properties of high energy production amplitudes in N=4 SUSY
We investigate analytic properties of the six point planar amplitude in N=4
SUSY at the multi-Regge kinematics for final state particles. For inelastic
processes the Steinmann relations play an important role because they give a
possibility to fix the phase structure of the Regge pole and Mandelstam cut
contributions. These contributions have the Moebius invariant form in the
transverse momentum subspace. The analyticity and factorization constraints
allow us to reproduce the two-loop correction to the 6-point BDS amplitude in
N=4 SUSY obtained earlier in the leading logarithmic approximation with the use
of the s-channel unitarity. The exponentiation hypothesis for the remainder
function in the multi-Regge kinematics is also investigated. The 6-point
amplitude in LLA can be completely reproduced from the BDS ansatz with the use
of the analyticity and Regge factorization.Comment: To appear in the proceedings of 16th International Seminar on High
Energy Physics, QUARKS-2010, Kolomna, Russia, 6-12 June, 2010. 15 page
Graviton emission in Einstein-Hilbert gravity
The five-point amplitude for the scattering of two distinct scalars with the
emission of one graviton in the final state is calculated in exact kinematics
for Einstein-Hilbert gravity. The result, which satisfies the Steinmann
relations, is expressed in Sudakov variables, finding that it corresponds to
the sum of two gauge invariant contributions written in terms of a new two
scalar - two graviton effective vertex. A similar calculation is carried out in
Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one
extra gluon in the final state. The effective vertices which appear in both
cases are then evaluated in the multi-Regge limit reproducing the well-known
result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex
can be written as the product of two QCD gluon emission vertices, up to
corrections to preserve the Steinmann relations.Comment: 28 pages, LaTeX, feynmf. v2: typos corrected, reference added. Final
version to appear in Journal of High Energy Physic
Integrable spin chains and scattering amplitudes
In this review we show that the multi-particle scattering amplitudes in N=4
SYM at large Nc and in the multi-Regge kinematics for some physical regions
have the high energy behavior appearing from the contribution of the Mandelstam
cuts in the complex angular momentum plane of the corresponding t-channel
partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon
composite states in the adjoint representation of the gauge group SU(Nc). In
the leading logarithmic approximation (LLA) their contribution to the six point
amplitude is in full agreement with the known two-loop result.
The Hamiltonian for the Mandelstam states constructed from n gluons in LLA
coincides with the local Hamiltonian of an integrable open spin chain. We
construct the corresponding wave functions using the integrals of motion and
the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A.
Volovich (ed
Increase of geostationary orbit efficiency in the Ku band based on changes of ITU threshold values
The article is devoted to the estimation of threshold values, regulated by ITU, which determine the necessity of satellite networks coordination in the Ku band. Maximum capacity of geostationary orbit (GEO) for different diameters of earth station antennas, operating in standard DVB-S2 accounting the limitations caused by the parameters of existing satellite networks equipment, is determined. Optimal values of satellites’ orbital separation, relative increase in allowable noise ∆T/T and the signal to single-interference ratio C/I were identified for maximum GEO capacity
Baxter Equation for the QCD Odderon
The Hamiltonian derived by Bartels, Kwiecinski and Praszalowicz for the study
of high-energy QCD in the generalized logarithmic approximation was found to
correspond to the Hamiltonian of an integrable spin chain. We study the
odderon Hamiltonian corresponding to three sites by means of the Bethe Ansatz
approach. We rewrite the Baxter equation, and consequently the Bethe Ansatz
equations, as a linear triangular system. We derive a new expression for the
eigenvectors and the eigenvalues, and discuss the quantization of the conserved
quantities.Comment: 14 pages, latex file, one figur
BFKL approach and 2->5 MHV amplitude
We study MHV amplitude for the 2 -> 5 scattering in the multi-Regge
kinematics. The Mandelstam cut correction to the BDS amplitude is calculated in
the leading logarithmic approximation (LLA) and the corresponding remainder
function is given to any loop order in a closed integral form. We show that the
LLA remainder function at two loops for 2 -> 5 amplitude can be written as a
sum of two 2 -> 4 remainder functions due to recursive properties of the
leading order impact factors. We also make some generalizations for the MHV
amplitudes with more external particles. The results of the present study are
in agreement with all leg two loop symbol derived by Caron-Huot as shown in a
parallel paper of one of the authors with collaborators.Comment: 24 pages, 17 figure
Analyticity and crossing symmetry of the eikonal amplitudes in gauge theories
After a brief review and a more refined analysis of some relevant analyticity
properties (when going from Minkowskian to Euclidean theory) of the high-energy
parton-parton and hadron-hadron scattering amplitudes in gauge theories,
described nonperturbatively, in the eikonal approximation, by certain
correlation functions of two Wilson lines or two Wilson loops near the light
cone, we shall see how these same properties lead to a nice geometrical
interpretation of the crossing symmetry between quark-quark and quark-antiquark
eikonal amplitudes and also between loop-loop eikonal amplitudes. This relation
between Minkowskian-to-Euclidean analyticity properties and crossing symmetry
is discussed in detail and explicitly tested in the first orders of
perturbation theory. Some nonperturbative examples existing in the literature
are also discussed.Comment: Completely revised version with new comments, new references and new
figures; 37 pages + 5 figure
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