pith. sign in

arxiv: 0907.2276 · v2 · pith:75MICVJMnew · submitted 2009-07-14 · ✦ hep-th

The Tree Formula for MHV Graviton Amplitudes

Dung Nguyen , Marcus Spradlin , Anastasia Volovich , Congkao Wen This is my paper
classification ✦ hep-th
keywords formulacancellationsratherspacetreeabsenceamplitudeamplitudes
0
0 comments X
read the original abstract

We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level. Some of the more interesting features of the formula, which set it apart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons--making it in a sense a truly gravitational formula, rather than a recycled Yang-Mills result, and the fact that it simultaneously manifests both S_{n-2} symmetry as well as large-z behavior that is O(1/z^2) term-by-term, without relying on delicate cancellations. The formula is seemingly related to others by an enormous simplification provided by O(n^n) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that are non-obvious in physical space become manifest.

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 12 Pith papers

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

  1. Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams

    hep-th 2024-11 unverdicted novelty 7.0

    Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.

  2. Tree and $1$-loop fundamental BCJ relations from soft theorems

    hep-th 2023-05 unverdicted novelty 7.0

    Derives the fundamental BCJ relation at tree level from soft theorems in bi-adjoint scalar theory, generalizes it to 1-loop integrands, and uses it to explain Adler zeros in other scalar theories.

  3. On soft factors and transmutation operators

    hep-th 2024-06 unverdicted novelty 6.0

    Reconstruction of known soft factors via transmutation operators and proof of nonexistence of higher-order universal soft factors for YM and GR amplitudes.

  4. Constructing tree amplitudes of scalar EFT from double soft theorem

    hep-th 2024-06 unverdicted novelty 6.0

    A method constructs tree amplitudes of scalar EFTs from the double soft theorem by determining the explicit double soft factor during the construction process.

  5. Multi-trace YMS amplitudes from soft behavior

    hep-th 2024-01 unverdicted novelty 6.0

    Derives expansion formulas for multi-trace YMS amplitudes bottom-up from soft gluon and scalar behaviors.

  6. Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem

    hep-th 2023-11 unverdicted novelty 6.0

    A recursive construction expands tree YM amplitudes to YMS and BAS amplitudes from soft theorems while preserving gauge invariance at each step.

  7. 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.

  8. 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...

  9. New recursive construction for tree NLSM and SG amplitudes, and new understanding of enhanced Adler zero

    hep-th 2023-10 unverdicted novelty 5.0

    Recursive construction of off-shell NLSM and SG tree amplitudes from bootstrapped low-point ones via universal soft behaviors, automatically producing enhanced Adler zeros on-shell.

  10. Note on tree NLSM amplitudes and soft theorems

    hep-th 2023-06 unverdicted novelty 5.0

    The paper constructs general tree NLSM amplitudes via an expanded formula enforced by Adler zero universality and derives the corresponding double soft factors.

  11. Tree level amplitudes from soft theorems

    hep-th 2022-12 unverdicted novelty 5.0

    Tree-level amplitudes for Yang-Mills-scalar, pure Yang-Mills, Einstein-Yang-Mills and gravitational theories are reconstructed from soft theorems, universality of soft factors and double copy, with explicit soft facto...

  12. Towards tree Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions

    hep-th 2024-06 unverdicted novelty 4.0

    Extends soft-behavior approach to construct tree YM and YMS amplitudes with F^3 (and F^3+F^4) insertions as universal expansions, plus a conjectured general formula for higher-mass-dimension YM amplitudes from ordinary ones.