1,621 research outputs found
Deformed Spectral Representation of the BFKL Kernel and the Bootstrap for Gluon Reggeization
We investigate the space of functions in which the BFKL kernel acts. For the
amplitudes which describe the scattering of colorless projectiles it is
convenient to define, in transverse coordinates, the Moebius space in which the
solutions to the BFKL equation vanish as the coordinates of the two reggeized
gluons coincide. However, in order to fulfill the bootstrap relation for the
BFKL kernel it is necessary to modify the space of functions. We define and
investigate a new space of functions and show explicitly that the bootstrap
relation is valid for the corresponding spectral form of the kernel. We
calculate the generators of the resulting deformed representation of the
sl(2,C) algebra.Comment: 22 pages, 1 figur
Fronts in passive scalar turbulence
The evolution of scalar fields transported by turbulent flow is characterized
by the presence of fronts, which rule the small-scale statistics of scalar
fluctuations. With the aid of numerical simulations, it is shown that: isotropy
is not recovered, in the classical sense, at small scales; scaling exponents
are universal with respect to the scalar injection mechanisms; high-order
exponents saturate to a constant value; non-mature fronts dominate the
statistics of intense fluctuations. Results on the statistics inside the
plateaux, where fluctuations are weak, are also presented. Finally, we analyze
the statistics of scalar dissipation and scalar fluxes.Comment: 18 pages, 27 figure
Semiclassical solution to the BFKL equation with massive gluons
In this paper we proceed to study the high energy behavior of a scattering
amplitudes in the Yang-Mills theory with the Higgs mechanism for the gauge
boson mass. The spectrum of the -plane singularities of the -channel
partial waves, and corresponding eigenfunctions of the BFKL equation in leading
log approximation (LLA), were previously calculated by us numerically in
arXiv:1401.4671 . Here we develop a semiclassical approach and investigate the
influence of the impact parameter exponential decrease, existing in this model,
on the high energy asymptotic behaviour of the scattering amplitude. This
approach is much simpler than the numerical calculations, and reproduces our
earlier numerical results. The analytical (semianalytical) solutions which have
been found in this paper, can be used to incorporate correctly the large impact
parameter behavior in the framework of CGC/saturation approach. This behaviour
is interesting as provides the high energy amplitude for the electroweak
theory, which can be measured experimentally.Comment: 22 pages, 13 Figure
Off-Shell Scattering Amplitudes for WW Scattering and the Role of the Photon Pole
We derive analytic expressions for high energy off-shell scattering
amplitudes of weak vector bosons. They are obtained from six fermion final
states in processes of the type . As an application we reconsider the
unitarity bounds on the Higgs mass. Particular attention is given to the role
of the photon exchange which has not been considered in earlier investigations;
we find that the photon weakens the bound of the Higgs mass.Comment: 16 pages, 8 figure
Effective action for the Regge processes in gravity
It is shown, that the effective action for the reggeized graviton
interactions can be formulated in terms of the reggeon fields and
and the metric tensor in such a way, that it is local in
the rapidity space and has the property of general covariance. The
corresponding effective currents and satisfy the
Hamilton-Jacobi equation for a massless particle moving in the gravitational
field. These currents are calculated explicitly for the shock wave-like fields
and a variation principle for them is formulated. As an application, we
reproduce the effective lagrangian for the multi-regge processes in gravity
together with the graviton Regge trajectory in the leading logarithmic
approximation with taking into account supersymmetric contributions.Comment: 39 page
Reggeized Gluons with a Running Coupling Constant
The equation for two reggeized gluons in the vacuum channel is generalized to
take into account the running QCD coupling constant on the basis of the
bootstrap condition for gluon reggeization. Both the gluon trajectory as a
function of momentum and the interaction as a function of distance grow like
in the ultraviolet. The resulting equation depends on the
confinement region. With a simple parametrization of its influence by an
effective gluon mass the pomeron intercept turns out much smaller than for a
fixed coupling constant (the BFKL pomeron).Comment: 9 pages, LaTeX, US-FT/12-9
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
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