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An Algebraic Approach to the Scattering Equations

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arxiv 1509.04483 v1 pith:6QIXARFZ submitted 2015-09-15 hep-th

Rijun Huang , Junjie Rao , Bo Feng , Yang-Hui He This is my paper · ORCID
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keywords scatteringalgebraicamplitudesapproachequationsmethodalgebraalgorithmic
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We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

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    The complete 207-dimensional family of one-loop five-gluon BCJ numerator coefficients is reconstructed exactly, and every direction in that family is shown to be invisible to the specified color-ring observable.

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