21,070 research outputs found
Evaluating single-scale and/or non-planar diagrams by differential equations
We apply a recently suggested new strategy to solve differential equations
for Feynman integrals. We develop this method further by analyzing asymptotic
expansions of the integrals. We argue that this allows the systematic
application of the differential equations to single-scale Feynman integrals.
Moreover, the information about singular limits significantly simplifies
finding boundary constants for the differential equations. To illustrate these
points we consider two families of three-loop integrals. The first are
form-factor integrals with two external legs on the light cone. We introduce
one more scale by taking one more leg off-shell, . We analytically
solve the differential equations for the master integrals in a Laurent
expansion in dimensional regularization with . Then we show
how to obtain analytic results for the corresponding one-scale integrals in an
algebraic way. An essential ingredient of our method is to match solutions of
the differential equations in the limit of small to our results at
and to identify various terms in these solutions according to
expansion by regions. The second family consists of four-point non-planar
integrals with all four legs on the light cone. We evaluate, by differential
equations, all the master integrals for the so-called graph consisting of
four external vertices which are connected with each other by six lines. We
show how the boundary constants can be fixed with the help of the knowledge of
the singular limits. We present results in terms of harmonic polylogarithms for
the corresponding seven master integrals with six propagators in a Laurent
expansion in up to weight six.Comment: 27 pages, 2 figure
Element gain drifts as an imaging dynamic range limitation in PAF-based interferometers
Interferometry with phased-array feeds (PAFs) presents new calibration
challenges in comparison with single-pixel feeds. In particular, temporal
instability of the compound beam patterns due to element gain drifts (EGDs) can
produce calibration artefacts in interferometric images. To translate imaging
dynamic range requirements into PAF hardware and calibration requirements, we
must learn to relate EGD levels to imaging artefact levels. We present a
MeqTrees-based simulations framework that addresses this problem, and apply it
to the APERTIF prototype currently in development for the WSRT.Comment: 4 pages, 3 figures, poster presentation at the XXX URSI General
Assembly and Scientific Symposium (Istanbul, Turkey, August 13-20, 2011
A planar four-loop form factor and cusp anomalous dimension in QCD
We compute the fermionic contribution to the photon-quark form factor to
four-loop order in QCD in the planar limit in analytic form. From the divergent
part of the latter the cusp and collinear anomalous dimensions are extracted.
Results are also presented for the finite contribution. We briefly describe our
method to compute all planar master integrals at four-loop order.Comment: 19 pages, 3 figures, v2: typo in (2.3) fixed and coefficients in
(2.6) corrected; references added and correcte
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