1,695 research outputs found
Automatic Integral Reduction for Higher Order Perturbative Calculations
We present a program for the reduction of large systems of integrals to
master integrals. The algorithm was first proposed by Laporta; in this paper,
we implement it in MAPLE. We also develop two new features which keep the size
of intermediate expressions relatively small throughout the calculation. The
program requires modest input information from the user and can be used for
generic calculations in perturbation theory.Comment: 23 page
Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
We present a method to evaluate numerically Feynman diagrams directly from
their Feynman parameters representation. We first disentangle overlapping
singularities using sector decomposition. Threshold singularities are treated
with an appropriate contour deformation. We have validated our technique
comparing with recent analytic results for the gg->h two-loop amplitudes with
heavy quarks and scalar quarks.Comment: 8 pages, 3 figures; references added, version to appear in JHE
Global symmetries of Yang-Mills squared in various dimensions
Tensoring two on-shell super Yang-Mills multiplets in dimensions
yields an on-shell supergravity multiplet, possibly with additional matter
multiplets. Associating a (direct sum of) division algebra(s) with
each dimension we obtain formulae for the algebras
and of the U-duality group and its maximal
compact subgroup , respectively, in terms of the internal global symmetry
algebras of each super Yang-Mills theory. We extend our analysis to include
supergravities coupled to an arbitrary number of matter multiplets by allowing
for non-supersymmetric multiplets in the tensor product.Comment: 25 pages, 2 figures, references added, minor typos corrected, further
comments on sec. 2.4 included, updated to match version to appear in JHE
NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization
We evaluate all phase space master integrals which are required for the total
cross section of generic 2 -> 1 processes at NNLO as a series expansion in the
dimensional regulator epsilon. Away from the limit of threshold production, our
expansion includes one order higher than what has been available in the
literature. At threshold, we provide expressions which are valid to all orders
in terms of Gamma functions and hypergeometric functions. These results are a
necessary ingredient for the renormalization and mass factorization of
singularities in 2 -> 1 inclusive cross sections at NNNLO in QCD.Comment: 37 pages, plus 3 ancillary files containing analytic expressions in
Maple forma
The fully differential hadronic production of a Higgs boson via bottom quark fusion at NNLO
The fully differential computation of the hadronic production cross section
of a Higgs boson via bottom quarks is presented at NNLO in QCD. Several
differential distributions with their corresponding scale uncertainties are
presented for the 8 TeV LHC. This is the first application of the method of
non-linear mappings for NNLO differential calculations at hadron colliders.Comment: 27 pages, 13 figures, 1 lego plo
Cross-Order Relations in N=4 Supersymmetric Gauge Theories
The anti-de Sitter/conformal field theory duality conjecture raises the
question of how the perturbative expansion in the conformal field theory can
resum to a simple function. We exhibit a relation between the one-loop and
two-loop amplitudes whose generalization to higher-point and higher-loop
amplitudes would answer this question. We also provide evidence for the first
of these generalizations.Comment: 6 pages, talk given at the 3rd International Symposium on Quantum
Theory and Symmetries, Cincinnati, OH, Sept 10-14, 2003; v2: Mispositioned
figure in eqn. 1 fixe
Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of
Wilson-loop vacuum expectation values and scattering amplitudes. In this paper,
we investigate this correspondence at the diagram level. We find that one-loop
triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple
one- and two- parametric integrals over a single propagator in configuration
space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a
four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of
the configuration-space propagator and loop Feynman diagrams, we derive Feynman
parameterizations of complicated planar and non-planar Feynman diagrams which
simplify their evaluation. For illustration, we compute numerically a four-loop
hexagon scalar Feynman diagram.Comment: 20 pages, many figures. Two references added. Published versio
Numerical evaluation of loop integrals
We present a new method for the numerical evaluation of arbitrary loop
integrals in dimensional regularization. We first derive Mellin-Barnes integral
representations and apply an algorithmic technique, based on the Cauchy
theorem, to extract the divergent parts in the epsilon->0 limit. We then
perform an epsilon-expansion and evaluate the integral coefficients of the
expansion numerically. The method yields stable results in physical kinematic
regions avoiding intricate analytic continuations. It can also be applied to
evaluate both scalar and tensor integrals without employing reduction methods.
We demonstrate our method with specific examples of infrared divergent
integrals with many kinematic scales, such as two-loop and three-loop box
integrals and tensor integrals of rank six for the one-loop hexagon topology
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