Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories

Abstract

In this paper, we demonstrate that the factorizations for tree amplitudes in the double-cover framework, for various theories, can be generated from the gravity amplitude in the double-cover prescription. Our method employs differential operators proposed by Cheung, Shen and Wen. Using our method, the factorized formulae for amplitudes of Yang-Mills theory, special Yang-Mills-scalar theory, and bi-adjoint scalar theory, have been derived. The differential operators indicate some non-trivial relationships among factorizations for above theories, as can be understood through four angles which are factorization channels, pole-structures, gauge choices, as well as BCFW recursions.

On differential operators and unifying relations for 1-loop Feynman integrands

“…, −] at tree level is ensured by the factorization of tree amplitude, there is no harm to see how it realize. The following treatment is similar as that in [28]. Let us choose the formula of operator…”

Scattering of gravitons and spinning massive states from compact numerators

“…As an alternative to the diagrammatic rules and to gain more insight into the structure of amplitudes, we will now discuss an extension of the recurrence formula obtained in [106][107][108][109] (for formulas derived from on-shell recursion, see [126][127][128][129][130]). We found the recurrence formula by studying the double-cover approach and the properties of the reduced Pfaffian for gluons.…”