New Recursion Relations for Tree Amplitudes of Gluons

Details New Recursion Relations for Tree Amplitudes of Gluons New Recursion Relations for Tree Amplitudes of Gluons

2004-12-27

arxiv.org/abs/hep-th/0412308v3

Nucl.Phys.B715:499-522,2005

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, harvmac. 6 figures. v2: Fixed typos in (4.1), added symmetric form of the alternating-helicity eight-gluon amplitude

Scientific paper

10.1016/j.nuclphysb.2005.02.030

We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to build any amplitude in terms of three-gluon amplitudes only.

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