17,887 research outputs found
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
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
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
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model
Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry
In radio interferometry, observed visibilities are intrinsically sampled at
some interval in time and frequency. Modern interferometers are capable of
producing data at very high time and frequency resolution; practical limits on
storage and computation costs require that some form of data compression be
imposed. The traditional form of compression is a simple averaging of the
visibilities over coarser time and frequency bins. This has an undesired side
effect: the resulting averaged visibilities "decorrelate", and do so
differently depending on the baseline length and averaging interval. This
translates into a non-trivial signature in the image domain known as
"smearing", which manifests itself as an attenuation in amplitude towards
off-centre sources. With the increasing fields of view and/or longer baselines
employed in modern and future instruments, the trade-off between data rate and
smearing becomes increasingly unfavourable. In this work we investigate
alternative approaches to low-loss data compression. We show that averaging of
the visibility data can be treated as a form of convolution by a boxcar-like
window function, and that by employing alternative baseline-dependent window
functions a more optimal interferometer smearing response may be induced. In
particular, we show improved amplitude response over a chosen field of
interest, and better attenuation of sources outside the field of interest. The
main cost of this technique is a reduction in nominal sensitivity; we
investigate the smearing vs. sensitivity trade-off, and show that in certain
regimes a favourable compromise can be achieved. We show the application of
this technique to simulated data from the Karl G. Jansky Very Large Array (VLA)
and the European Very-long-baseline interferometry Network (EVN)
Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)
We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit
expression for the Drinfeld associator. We restrict to the case of the
fundamental representation of . Several tests of the results are
presented. It can be explicitly seen that components of this solution for the
associator coincide with certain components of WZW conformal block for primary
fields. We introduce the symmetrized version of the Drinfeld associator by
dropping the odd terms. The symmetrized associator gives the same knot
invariants, but has a simpler structure and is fully characterized by one
symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte
Magic identities for conformal four-point integrals
We propose an iterative procedure for constructing classes of off-shell
four-point conformal integrals which are identical. The proof of the identity
is based on the conformal properties of a subintegral common for the whole
class. The simplest example are the so-called `triple scalar box' and `tennis
court' integrals. In this case we also give an independent proof using the
method of Mellin--Barnes representation which can be applied in a similar way
for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of
contact terms. Typo correcte
Computing the Loewner driving process of random curves in the half plane
We simulate several models of random curves in the half plane and numerically
compute their stochastic driving process (as given by the Loewner equation).
Our models include models whose scaling limit is the Schramm-Loewner evolution
(SLE) and models for which it is not. We study several tests of whether the
driving process is Brownian motion. We find that just testing the normality of
the process at a fixed time is not effective at determining if the process is
Brownian motion. Tests that involve the independence of the increments of
Brownian motion are much more effective. We also study the zipper algorithm for
numerically computing the driving function of a simple curve. We give an
implementation of this algorithm which runs in a time O(N^1.35) rather than the
usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph
to conclusion section; improved figures cosmeticall
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