270 research outputs found
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
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
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
Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape
We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length
Baxter's Q-operator for the homogeneous XXX spin chain
Applying the Pasquier-Gaudin procedure we construct the Baxter's Q-operator
for the homogeneous XXX model as integral operator in standard representation
of SL(2). The connection between Q-operator and local Hamiltonians is
discussed. It is shown that operator of Lipatov's duality symmetry arises
naturally as leading term of the asymptotic expansion of Q-operator for large
values of spectral parameter.Comment: 23 pages, Late
Methoden van grondstomen, 1969 - 1970
We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of eigenfunctions with positive eigenvalues, , together with a small contribution from a continuum of eigenfunctions with negative , provide an excellent description of high-precision HERA data in the region, . The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples completely or almost completely from the proton. This suggests that there exists an additional ground state, which is naturally saturated and may have the properties of the soft pomeron
The Pomeron and Gauge/String Duality
The traditional description of high-energy small-angle scattering in QCD has
two components -- a soft Pomeron Regge pole for the tensor glueball, and a hard
BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string
duality, we present a coherent treatment of the Pomeron. In large-N QCD-like
theories, we use curved-space string-theory to describe simultaneously both the
BFKL regime and the classic Regge regime. The problem reduces to finding the
spectrum of a single j-plane Schrodinger operator. For ultraviolet-conformal
theories, the spectrum exhibits a set of Regge trajectories at positive t, and
a leading j-plane cut for negative t, the cross-over point being
model-dependent. For theories with logarithmically-running couplings, one
instead finds a discrete spectrum of poles at all t, where the Regge
trajectories at positive t continuously become a set of slowly-varying and
closely-spaced poles at negative t. Our results agree with expectations for the
BFKL Pomeron at negative t, and with the expected glueball spectrum at positive
t, but provide a framework in which they are unified. Effects beyond the single
Pomeron exchange are briefly discussed.Comment: 68 pages, uses JHEP3.cls, utphys.bst; references added, typos
corrected, and clarifying remarks adde
Analogs of noninteger powers in general analytic QCD
In contrast to the coupling parameter in the usual perturbative QCD (pQCD),
the coupling parameter in the analytic QCD models has cuts only on the negative
semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus
reflecting correctly the analytic structure of the spacelike observables. The
Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes
the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the
pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to
evaluate in MA the physical QCD quantities whose perturbation expansion
involves noninteger powers of the pQCD coupling, a specific method of
construction of MA analogs of noninteger pQCD powers was developed by Bakulev,
Mikhailov and Stefanis (BMS). We present a construction, applicable now in any
analytic QCD model, of analytic analogs of noninteger pQCD powers; this method
generalizes the BMS approach obtained in the framework of MA. We need to know
only the discontinuity function of the analytic coupling (the analog of the
pQCD coupling) along its cut in order to obtain the analytic analogs of the
noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian)
counterparts. As an illustration, we apply the method to the evaluation of the
width for the Higgs decay into b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne
Leading-Log Effects in the Resonance Electroweak Form Factors
We study log corrections to inelastic scattering at high Bjorken x for Q^2
from 1 to 21 GeV^2. At issue is the presence of log corrections, which can be
absent if high x scattering has damped gluon radiation. We find logarithmic
correction of the scaling curve extrapolated to low Q^2 improves the duality
between it and the resonance plus background data in the Delta region,
indicating log corrections exist in the data. However, at W > 2 GeV and high x,
the data shows a (1-x)^3 form. Log corrections in one situation but not in
another can be reconciled by a W- or Q^2- dependent higher twist correction.Comment: 13 pages, report nos. RPI-94-N90 and WM-94-106, revtex, two figures
(available by fax or post
The BFKL Pomeron in 2+1 Dimensional QCD
We investigate the high-energy scattering in the spontaneously broken Yang -
Mills gauge theory in 2+1 space--time dimensions and present the exact solution
of the leading BFKL equation. The solution is constructed in terms of
special functions using the earlier results of two of us (L.N.L. and L.S.). The
analytic properties of the -channel partial wave as functions of the angular
momentum and momentum transfer have been studied. We find in the angular
momentum plane: (i) a Regge pole whose trajectory has an intercept larger than
1 and (ii) a fixed cut with the rightmost singularity located at . The
massive Yang - Mills theory can be considered as a theoretical model for the
(non-perturbative) Pomeron. We study the main structure and property of the
solution including the Pomeron trajectory at momentum transfer different from
zero. The relation to the results of M. Li and C-I. Tan for the massless case
is discussed.Comment: 28 pages LATEX, 3 EPS figures include
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