Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles

Abstract

Tree-level scattering amplitudes for gravitons, gluons and Goldstone particles in any dimensions are strongly constrained by basic principles, and they are intimately related to each other via various relations. We study two types of "universal expansions" with respect to gauge bosons and Goldstone bosons: the former express tree amplitudes in Einstein gravity (Yang-Mills) as linear combinations of single-trace Einstein-Yang-Mills (Yang-Mills-φ 3 ) amplitudes with coefficients given by Lorentz products of polarizations and momenta; the latter express tree amplitudes in non-linear sigma model, (Dirac-)Born-Infeld and a special Galileon theory, as linear combinations of singletrace mixed amplitudes with particles of lower "degree of Adler's zero" and coefficients given by products of Mandelstam variables. We trace the origin of gauge-theory expansions to the powerful uniqueness theorem based on gauge invariance, and expansions in effective field theories can be derived from gauge-theory ones via a special dimension reduction.

Transmutation operators and expansions for $1$-loop Feynman integrands

“…However, for the GR Feynman integrands without any color ordering, it is natural to expect a form without any special external leg. To realize the goal, we use the conclusion in [33] that if one impose the gauge invariance for all legs in a a a h n , then each term of the tree GR amplitude A , GR (a a a h n ∪ {+, −}) always contain a monomial in the form…”