118 research outputs found
Counting loop diagrams: computational complexity of higher-order amplitude evaluation
We discuss the computational complexity of the perturbative evaluation of
scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct
evaluation of the individual diagrams. For a self-interacting scalar theory, we
determine the complexity as a function of the number of external legs. We
describe a method for obtaining the number of topologically inequivalent
Feynman graphs containing closed loops, and apply this to one- and two-loop
amplitudes. We also compute the number of graphs weighted by their symmetry
factors, thus arriving at exact and asymptotic estimates for the average
symmetry factor of diagrams. We present results for the asymptotic number of
diagrams up to 10 loops, and prove that the average symmetry factor approaches
unity as the number of external legs becomes large.Comment: 27 pages, 17 table
SARGE: an algorithm for generating QCD-antennas
We present an algorithm to generate any number of random massless momenta in
phase space, with a distribution that contains the kinematical pole structure
that is typically found in multi-parton QCD-processes. As an application, we
calculate the cross-section of some \eplus\eminus \to partons processes, and
compare SARGE's performance with that of the uniform-phase space generator
RAMBO.Comment: 9 pages, affiliation correcte
Counting tree diagrams: asymptotic results for QCD-like theories
We discuss the enumeration of Feynman diagrams at tree order for processes
with external lines of different types. We show how this can be done by
iterating algebraic Schwinger-Dyson equations. Asymptotic estimates for very
many external lines are derived. Applications include QED, QCD and scalar QED,
and the asymptotic estimates are numerically confronted with the exact results.Comment: 16 page
Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD
We present a proof of the Britto-Cachazo-Feng-Witten tree-level recursion
relation for gluon amplitudes in QCD, based on a direct equivalence between
BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence
can be made explicit when working in a convenient gauge. We exhibit that gauge
invariance and the particular structure of Yang-Mills vertices guarantees the
validity of the BCFW construction.Comment: 24 pages, 33 figure
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