1,122 research outputs found
The Behaviour of the Green Function for the BFKL Pomeron with Running Coupling
We analyse here in LO the physical properties of the Green function solution
for the BFKL equation. We show that the solution obeys the orthonormality
conditions in the physical region and fulfills the completeness requirements.
The unintegrated gluon density is shown to consists of a set of few poles with
parameters which could be determined by comparison with the DIS data of high
precision
Indirect Evidence for New Physics at the 10 TeV Scale
We show that the supersymmetric extension of the Standard Model modifies the
structure of the low lying BFKL discrete pomeron states (DPS) which give a
sizable contribution to the gluon structure function in the HERA x and Q2
region. The comparison of the gluon density, determined within DPS with N=1
SUSY, with data favours a supersymmetry scale of the order of 10 TeV. The DPS
method described here could open a new window to the physics beyond the
Standard Model.Comment: 14 pages, 6 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
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
Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories
A long time ago, it has been conjectured that a Hamiltonian with a potential
of the form x^2+i v x^3, v real, has a real spectrum. This conjecture has been
generalized to a class of so-called PT symmetric Hamiltonians and some proofs
have been given. Here, we show by numerical investigation that the divergent
perturbation series can be summed efficiently by an order-dependent mapping
(ODM) in the whole complex plane of the coupling parameter v^2, and that some
information about the location of level crossing singularities can be obtained
in this way. Furthermore, we discuss to which accuracy the strong-coupling
limit can be obtained from the initially weak-coupling perturbative expansion,
by the ODM summation method. The basic idea of the ODM summation method is the
notion of order-dependent "local" disk of convergence and analytic continuation
by an order-dependent mapping of the domain of analyticity augmented by the
local disk of convergence onto a circle. In the limit of vanishing local radius
of convergence, which is the limit of high transformation order, convergence is
demonstrated both by numerical evidence as well as by analytic estimates.Comment: 11 pages; 12 figure
Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
In this second part of the treatment of instantons in quantum mechanics, the
focus is on specific calculations related to a number of quantum mechanical
potentials with degenerate minima. We calculate the leading multi-instanton
constributions to the partition function, using the formalism introduced in the
first part of the treatise [J. Zinn-Justin and U. D. Jentschura, e-print
quant-ph/0501136]. The following potentials are considered: (i) asymmetric
potentials with degenerate minima, (ii) the periodic cosine potential, (iii)
anharmonic oscillators with radial symmetry, and (iv) a specific potential
which bears an analogy with the Fokker-Planck equation. The latter potential
has the peculiar property that the perturbation series for the ground-state
energy vanishes to all orders and is thus formally convergent (the ground-state
energy, however, is nonzero and positive). For the potentials (ii), (iii), and
(iv), we calculate the perturbative B-function as well as the instanton
A-function to fourth order in g. We also consider the double-well potential in
detail, and present some higher-order analytic as well as numerical
calculations to verify explicitly the related conjectures up to the order of
three instantons. Strategies analogous to those outlined here could result in
new conjectures for problems where our present understanding is more limited.Comment: 55 pages, LaTeX; refs. to part I preprint update
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
Symmetry Properties of the Effective Action for High-Energy Scattering in QCD
We study the effective action describing high-energy scattering processes in
the multi-Regge limit of QCD, which should provide the starting point for a new
attempt to overcome the limitations of the leading logarithmic and the eikonal
approximations. The action can be obtained via simple graphical rules or by
integrating in the QCD functional integral over momentum modes of gluon and
quark fields that do not appear explicitely as scattering or exchanged
particles in the considered processes. The supersymmetry is used to obtain the
terms in the action involving quarks fields from the pure gluonic ones. We
observe a Weizs\"acker - Williams type relations between terms describing
scattering and production of particles.Comment: 37 pages LATEX, 1 Table and 7 figures using package FEYNMA
Anisotropy beta functions
The flow of couplings under anisotropic scaling of momenta is computed in
theory in 6 dimensions. It is shown that the coupling decreases as
momenta of two of the particles become large, keeping the third momentum fixed,
but at a slower rate than the decrease of the coupling if all three momenta
become large simultaneously. This effect serves as a simple test of effective
theories of high energy scattering, since such theories should reproduce these
deviations from the usual logarithmic scale dependence.Comment: uuencoded ps file, 6 page
- …