pith. sign in

arxiv: hep-th/0412308 · v3 · submitted 2004-12-27 · ✦ hep-th · hep-ph

New Recursion Relations for Tree Amplitudes of Gluons

classification ✦ hep-th hep-ph
keywords amplitudesamplitudegiverelationsrecursiontreebuildcompact
0
0 comments X
read the original abstract

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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Consistent Scattering Amplitudes, Yang-Mills, the Higgs Mechanism and the EFTs Beyond

    hep-th 2026-05 unverdicted novelty 7.0

    S-matrix consistency forces the complete gluon amplitude structure and requires Yang-Mills Lie algebra plus Higgs mechanism for unitarised massive vector boson scattering.

  2. String Theory from Maximal Supersymmetry

    hep-th 2026-01 unverdicted novelty 7.0

    Supersymmetry, R-symmetry, and positivity constrain planar 4d EFTs to match the open string Veneziano amplitude at tree level.

  3. A new recursion relation for tree-level NLSM amplitudes based on hidden zeros

    hep-th 2025-08 unverdicted novelty 6.0

    A recursion for NLSM tree amplitudes based on hidden zeros reproduces the Adler zero, generates amplitudes from Tr(φ³) via δ-shift, expands them into bi-adjoint scalars, and claims these plus factorization uniquely de...

  4. Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?

    hep-th 2026-04 unverdicted novelty 5.0

    Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.

  5. BCFW like recursion for Deformed Associahedron

    hep-th 2025-07 unverdicted novelty 5.0

    Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.

  6. Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits

    hep-th 2025-05 unverdicted novelty 5.0

    Extends a 2-split factorization approach to reproduce known leading and sub-leading soft theorems for Tr(φ³) and YM single-soft and NLSM double-soft amplitudes while deriving higher-order universal forms and a kinemat...