Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order g6
Year: 2026
Type: article
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.
Source: Journal of High Energy Physics
Author: M. Maniatis
Institution: University of Bío-Bío
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7221172833