S@M, a Mathematica Implementation of the SpinorFormalism Page: 2 of 52
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Theoretical understanding of background processes is essential to single out
interesting signals in the rich landscape of events which will take place at
the forthcoming CERN experiment, the Large Hadron Collider (LHC). Many
methods are available for computing Standard Model backgrounds at the lead-
ing order (LO) in perturbation theory [1-5], based either on automatic sum-
mation of tree-level Feynman diagram, or off-shell recursive algorithms for
currents [6-8]. But quantitative estimates for most processes require a calcu-
lation with next-to-leading order (NLO) accuracy - see for instance . NLO
calculations require knowledge of both virtual and real-radiation corrections
to the LO process. While the real-radiation corrections can be computed us-
ing tree-level techniques, the bottleneck for the availability of results with
NLO level accuracy [10-19] is the non-trivial evaluation of one-loop virtual
corrections. New approaches tackling the evaluation of one-loop multi-parton
amplitudes have recently been under intense development [16,17,20-51].
The spinor helicity formalism  for scattering amplitudes has proven an in-
valuable tool in perturbative computation since its development in the 1980's,
being responsible for the discovery of compact representations of tree and
loop amplitudes. Instead of Lorentz inner products of momenta, it relies on
the more fundamental spinor products. These neatly capture the analytic
properties of on-shell scattering amplitudes, like the factorization behavior
on multi-particle-channels. The recent boost in the progress of evaluating on-
shell scattering amplitudes is due to turning qualitative information on their
analytic properties into quantitative tools for computing them.
On-shell methods  restrict the propagating states to the physical ones and
the spinor-helicity formalism is therefore well suited to avoid the (intermedi-
ate) treatment of unphysical degrees of freedom whose effects disappear from
final results. Moreover, on-shell methods are tailored for the parallel treat-
ment of sets of diagrams which share a common kinematic structure, such as
multi-particle poles at tree-level and branch-cuts at loop-level [54, 55]. They
are therefore suitable for extracting analytic information from simpler am-
plitudes in a recursive/iterative fashion, since the singularities of scattering
amplitude are determined by lower-point amplitudes in the case of poles and
by lower-loop ones in the case of cuts [56-58].
On-shell methods were originally used in  and in the more recent sys-
tematized implementations for the completion of all six-gluon helicity am-
plitudes [30, 35, 36, 39, 41, 42, 46-48] and the calculation of the six-photon
amplitudes [31, 60] in agreement with the numerical results of [29, 33] and
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Maitre, D. & Mastrolia, P. S@M, a Mathematica Implementation of the SpinorFormalism, article, November 2, 2007; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc890820/m1/2/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.