Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica

We describe an efficient implementation of the BCFW recursion relations for tree-amplitudes in N = 4 super Yang-Mills, which can generate analytic formulae for general NkMHV colour-ordered helicity-amplitudes—which, in particular, includes all those of non-supersymmetric Yang-Mills. This note accompanies the public release of the Mathematica package bcfw, which can quickly (and automatically) generate these amplitudes in a form that should be easy to export to any computational framework of interest, or which can be evaluated directly within Mathematica given external states specified by four-momenta, spinor-helicity variables or momentum-twistors. Moreover, bcfw is able to solve the BCFW recursion relations using any one of a three-parameter family of recursive ‘schemes,’ leading to an extremely wide variety of distinct analytic representations of any particular amplitude. This flexibility is made possible by bcfw’s use of the momentum-twistor Grassmannian integral to describe all tree amplitudes; and this flexibility is accompanied by a remarkable increase in efficiency, leading to formulae that can be evaluated much faster—often by several orders of magnitude—than those previously derived using BCFW.

Files

Metadata

Work Title Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
Access
Open Access
Creators
  1. Jacob L. Bourjaily
License CC BY 4.0 (Attribution)
Work Type Article
Publisher
  1. arXiv
Publication Date November 1, 2010
Publisher Identifier (DOI)
  1. https://doi.org/10.48550/arXiv.1011.2447
Deposited November 21, 2024

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added tree_amplitudes_in_mathematica-1.pdf
  • Added Creator Jacob L. Bourjaily
  • Published
  • Updated