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.
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Work Title | Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica |
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License | CC BY 4.0 (Attribution) |
Work Type | Article |
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Publication Date | November 1, 2010 |
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Deposited | November 21, 2024 |
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