22,057 research outputs found
On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
One of the two existing strategies of resolving singularities of multifold
Mellin-Barnes integrals in the dimensional regularization parameter, or a
parameter of the analytic regularization, is formulated in a modified form. The
corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page
Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
We compute the leading-color (planar) three-loop four-point amplitude of N=4
supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent
expansion about epsilon = 0 including the finite terms. The amplitude was
constructed previously via the unitarity method, in terms of two Feynman loop
integrals, one of which has been evaluated already. Here we use the
Mellin-Barnes integration technique to evaluate the Laurent expansion of the
second integral. Strikingly, the amplitude is expressible, through the finite
terms, in terms of the corresponding one- and two-loop amplitudes, which
provides strong evidence for a previous conjecture that higher-loop planar N =
4 amplitudes have an iterative structure. The infrared singularities of the
amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on
resummation. Based on the four-point result and the exponentiation of infrared
singularities, we give an exponentiated ansatz for the maximally
helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole
in the four-point amplitude determines the soft, or cusp, anomalous dimension
at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a
prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the
leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and
Vogt. Following similar logic, we are able to predict a term in the three-loop
quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words
about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on
multiloop ansatz; remark that form-factor prediction is now confirmed by
other work; minor typos correcte
Fermionic decays of scalar leptoquarks and scalar gluons in the minimal four color symmetry model
Fermionic decays of the scalar leptoquarks
and of the scalar gluons predicted by the four color symmetry
model with the Higgs mechanism of the quark-lepton mass splitting are
investigated. Widths and branching ratios of these decays are calculated and
analysed in dependence on coupling constants and on masses of the decaying
particles. It is shown that the decays are
dominant with the widths of order of a few GeV for TeV and with
the total branching ratios close to 1. In the case of the dominant
scalar leptoquark decays are S_1^{(+)}\to cl_j^+, S_1^{(-)}\to \nu_i\tilde b,
S_m\to b\l_j^+, S_m\to c\tilde \nu_j with the total branching ratios
,
and A
search for such decays at the LHC and Tevatron may be of interest.Comment: 11 pages, 1 figure, 1 table, to be published in Modern Physics
Letters
Asymptotic Bound-state Model for Feshbach Resonances
We present an Asymptotic Bound-state Model which can be used to accurately
describe all Feshbach resonance positions and widths in a two-body system. With
this model we determine the coupled bound states of a particular two-body
system. The model is based on analytic properties of the two-body Hamiltonian,
and on asymptotic properties of uncoupled bound states in the interaction
potentials. In its most simple version, the only necessary parameters are the
least bound state energies and actual potentials are not used. The complexity
of the model can be stepwise increased by introducing threshold effects,
multiple vibrational levels and additional potential parameters. The model is
extensively tested on the 6Li-40K system and additional calculations on the
40K-87Rb system are presented.Comment: 13 pages, 8 figure
Nodal Domain Statistics for Quantum Maps, Percolation and SLE
We develop a percolation model for nodal domains in the eigenvectors of
quantum chaotic torus maps. Our model follows directly from the assumption that
the quantum maps are described by random matrix theory. Its accuracy in
predicting statistical properties of the nodal domains is demonstrated by
numerical computations for perturbed cat maps and supports the use of
percolation theory to describe the wave functions of general hamiltonian
systems, where the validity of the underlying assumptions is much less clear.
We also demonstrate that the nodal domains of the perturbed cat maps obey the
Cardy crossing formula and find evidence that the boundaries of the nodal
domains are described by SLE with close to the expected value of 6,
suggesting that quantum chaotic wave functions may exhibit conformal invariance
in the semiclassical limit.Comment: 4 pages, 5 figure
Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas
Gyrokinetic field theory is addressed in the context of a general
Hamiltonian. The background magnetic geometry is static and axisymmetric, and
all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian
or in free field terms. Equations for the fields are given by functional
derivatives. The symmetry through the Hamiltonian with time and toroidal angle
invariance of the geometry lead to energy and toroidal momentum conservation.
In various levels of ordering against fluctuation amplitude, energetic
consistency is exact. The role of this in underpinning of conservation laws is
emphasised. Local transport equations for the vorticity, toroidal momentum, and
energy are derived. In particular, the momentum equation is shown for any form
of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic (MHD)
form when long wavelength approximations are taken in the Hamiltonian. Several
currently used forms, those which form the basis of most global simulations,
are shown to be well defined within the gyrokinetic field theory and energetic
consistency.Comment: RevTeX 4, 47 pages, no figures, revised version updated following
referee comments (discussion more strictly correct/consistent, 4 references
added, results unchanged as they depend on consistency of the theory),
resubmitted to Physics of Plasma
Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model
The 7--particle form factors of the fundamental spin field of the O(3)
nonlinear --model are constructed. We calculate the corresponding
contribution to the spin--spin correlation function, and compare with
predictions from the spectral density scaling hypothesis. The resulting
approximation to the spin--spin correlation function agrees well with that
computed in renormalized (asymptotically free) perturbation theory in the
expected energy range. Further we observe simple lower and upper bounds for the
sum of the absolute square of the form factors which may be of use for analytic
estimates.Comment: 14 pages, 3 figures, late
Infrared study of spin-Peierls compound alpha'-NaV2O5
Infrared reflectance of alpha'-NaV2O5 single crystals in the frequency range
from 50 cm-1 to 10000 cm-1 was studied for a, b and c-polarisations. In
addition to phonon modes identification, for the a-polarised spectrum a broad
continuum absorption in the range of 1D magnetic excitation energies was found.
The strong near-IR absorption band at 0.8 eV shows a strong anisotropy with
vanishing intensity in c-polarisation. Activation of new phonons due to the
lattice dimerisation were detected below 35K as well as pretransitional
structural fluctuations up to 65K.Comment: 3 pages, 2 figures, 1 table. Contributed paper for the SCES'98 (15-18
July 1998, Paris). To be published in Physica
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