Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order g6
- 1Universidad del Bío-Bío
Abstract
A bstract : We formulate a systematic on-shell construction of perturbative amplitudes by combining the Feynman–tree theorem with BCFW recursion. Amplitudes are built entirely from on-shell tree amplitudes generated by BCFW and are supplemented by additional unobservable state-conjugate on-shell pairs, called vacuum pairs, whose momenta are integrated over Lorentz-invariant phase space. At fixed coupling order, the contributing tree amplitudes are classified by polygon bookkeeping, while their products form forests whose relative signs are fixed by inclusion–exclusion. We show that these signs coincide with the signs assigned by the full Feynman–tree-theorem cut expansion, so that the construction reproduces the ordinary perturbative loop expansion order by order. The dynamical tree input consists of the allowed three-point on-shell amplitudes; the particle spectrum, couplings, and color data are taken as given, and no off-shell object is introduced at any stage.
As a nontrivial test of this equivalence, we study the four-gluon all-plus amplitude through orders g ⁴ and g ⁶ . The on-shell construction reproduces the finite rational one-loop primitive amplitude and the known bare planar and non-planar two-loop primitive integrands, including the bow-tie terms in the planar primitive.
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BibTeX
@article{maniatis2026perturbative,
title = {{Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order g6}},
author = {M. Maniatis},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)090},
url = {https://link.springer.com/10.1007/JHEP10(2026)090},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order g6
AU - M. Maniatis
PY - 2026
DA - 2026/10/08
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)090
UR - https://link.springer.com/10.1007/JHEP10(2026)090
AB - A bstract : We formulate a systematic on-shell construction of perturbative amplitudes by combining the Feynman–tree theorem with BCFW recursion. Amplitudes are built entirely from on-shell tree amplitudes generated by BCFW and are supplemented by additional unobservable state-conjugate on-shell pairs, called vacuum pairs, whose momenta are integrated over Lorentz-invariant phase space. At fixed coupling order, the contributing tree amplitudes are classified by polygon bookkeeping, while their products form forests whose relative signs are fixed by inclusion–exclusion. We show that these signs coincide with the signs assigned by the full Feynman–tree-theorem cut expansion, so that the construction reproduces the ordinary perturbative loop expansion order by order. The dynamical tree input consists of the allowed three-point on-shell amplitudes; the particle spectrum, couplings, and color data are taken as given, and no off-shell object is introduced at any stage. As a nontrivial test of this equivalence, we study the four-gluon all-plus amplitude through orders g ⁴ and g ⁶ . The on-shell construction reproduces the finite rational one-loop primitive amplitude and the known bare planar and non-planar two-loop primitive integrands, including the bow-tie terms in the planar primitive.
SN - 1029-8479
ER -