479 research outputs found
Azurite: An algebraic geometry based package for finding bases of loop integrals
For any given Feynman graph, the set of integrals with all possible powers of
the propagators spans a vector space of finite dimension. We introduce the
package {\sc Azurite} ({\bf A ZUR}ich-bred method for finding master {\bf
I}n{\bf TE}grals), which efficiently finds a basis of this vector space. It
constructs the needed integration-by-parts (IBP) identities on a set of
generalized-unitarity cuts. It is based on syzygy computations and analyses of
the symmetries of the involved Feynman diagrams and is powered by the computer
algebra systems {\sc Singular} and {\sc Mathematica}. It can moreover
analytically calculate the part of the IBP identities that is supported on the
cuts.Comment: Version 1.1.0 of the package Azurite, with parallel computations. It
can be downloaded from
https://bitbucket.org/yzhphy/azurite/raw/master/release/Azurite_1.1.0.tar.g
SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
SecDec is a program which can be used for the factorization of dimensionally
regulated poles from parametric integrals, in particular multi-loop integrals,
and the subsequent numerical evaluation of the finite coefficients. Here we
present version 3.0 of the program, which has major improvements compared to
version 2: it is faster, contains new decomposition strategies, an improved
user interface and various other new features which extend the range of
applicability.Comment: 46 pages, version to appear in Comput.Phys.Com
On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations
An improved method is presented for the numerical evaluation of multi-loop
integrals in dimensional regularization. The technique is based on
Mellin-Barnes representations, which have been used earlier to develop
algorithms for the extraction of ultraviolet and infrared divergencies. The
coefficients of these singularities and the non-singular part can be integrated
numerically. However, the numerical integration often does not converge for
diagrams with massive propagators and physical branch cuts. In this work,
several steps are proposed which substantially improve the behavior of the
numerical integrals. The efficacy of the method is demonstrated by calculating
several two-loop examples, some of which have not been known before.Comment: 13 pp. LaTe
Numerical Loop-Tree Duality: contour deformation and subtraction
We introduce a novel construction of a contour deformation within the
framework of Loop-Tree Duality for the numerical computation of loop integrals
featuring threshold singularities in momentum space. The functional form of our
contour deformation automatically satisfies all constraints without the need
for fine-tuning. We demonstrate that our construction is systematic and
efficient by applying it to more than 100 examples of finite scalar integrals
featuring up to six loops. We also showcase a first step towards handling
non-integrable singularities by applying our work to one-loop infrared
divergent scalar integrals and to the one-loop amplitude for the ordered
production of two and three photons. This requires the combination of our
contour deformation with local counterterms that regulate soft, collinear and
ultraviolet divergences. This work is an important step towards computing
higher-order corrections to relevant scattering cross-sections in a fully
numerical fashion.Comment: 87 page
Maximal Cuts in Arbitrary Dimension
We develop a systematic procedure for computing maximal unitarity cuts of
multiloop Feynman integrals in arbitrary dimension. Our approach is based on
the Baikov representation in which the structure of the cuts is particularly
simple. We examine several planar and nonplanar integral topologies and
demonstrate that the maximal cut inherits IBPs and dimension shift identities
satisfied by the uncut integral. Furthermore, for the examples we calculated,
we find that the maximal cut functions from different allowed regions, form the
Wronskian matrix of the differential equations on the maximal cut.Comment: typos corrected, more references adde
Automatic Computation of Feynman Diagrams
Quantum corrections significantly influence the quantities observed in modern
particle physics. The corresponding theoretical computations are usually quite
lengthy which makes their automation mandatory. This review reports on the
current status of automatic calculation of Feynman diagrams in particle
physics. The most important theoretical techniques are introduced and their
usefulness is demonstrated with the help of simple examples. A survey over
frequently used programs and packages is provided, discussing their abilities
and fields of applications. Subsequently, some powerful packages which have
already been applied to important physical problems are described in more
detail. The review closes with the discussion of a few typical applications for
the automated computation of Feynman diagrams, addressing current physical
questions like properties of the and Higgs boson, four-loop corrections to
renormalization group functions and two-loop electroweak corrections.Comment: Latex, 62 pages. Typos corrected, references updated and some
comments added. Vertical offset changed. The complete paper is also available
via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or
via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints
LUSIFER: a LUcid approach to SIx-FERmion production
LUSIFER is a Monte Carlo event generator for all processes e+e-->6fermions,
which is based on the multi-channel Monte Carlo integration technique and
employs the full set of tree-level diagrams. External fermions are taken to be
massless, but can be arbitrarily polarized. The calculation of the helicity
amplitudes and of the squared matrix elements is presented in a compact way.
Initial-state radiation is included at the leading logarithmic level using the
structure-function approach. The discussion of numerical results contains a
comprehensive list of cross sections relevant for a 500GeV collider, including
a tuned comparison to results obtained with the combination of the WHIZARD and
MADGRAPH packages as far as possible. Moreover, for off-shell top-quark pair
production and the production of a Higgs boson in the intermediate mass range
we additionally discuss some phenomenologically interesting distributions.
Finally, we numerically analyze the effects of gauge-invariance violation by
comparing various ways of introducing decay widths of intermediate top quarks,
gauge and Higgs bosons.Comment: 39 pages, latex, 14 postscript files, some minor misprints corrected,
version to appear in Nucl.Phys.
Reduction and evaluation of two-loop graphs with arbitrary masses
We describe a general analytic-numerical reduction scheme for evaluating any
2-loop diagrams with general kinematics and general renormalizable
interactions, whereby ten special functions form a complete set after tensor
reduction. We discuss the symmetrical analytic structure of these special
functions in their integral representation, which allows for optimized
numerical integration. The process Z -> bb is used for illustration, for which
we evaluate all the 3-point, non-factorizable g^2*alpha_s mixed electroweak-QCD
graphs, which depend on the top quark mass. The isolation of infrared
singularities is detailed, and numerical results are given for all two-loop
three-point graphs involved in this process
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