Abstract
We show how the S-matrix of an extended theory of gravity defined by its three-point amplitudes can be constructed by demanding factorisation. The resultant S-matrix has tree amplitudes obeying the same soft singularity theorems as Einstein gravity including the sub-sub-leading terms.
Highlights
Scattering amplitudes are traditionally defined from a quantum field theory and the resulting Feynman vertices and Feynman diagrams
It is not very useful to define a theory by specifying the entire S-matrix explicitly but it is an important question whether the S-matrix can be defined from a minimal set of data and rules i.e. a “diagrammar” [1]
We show that a similar construction can be used for an extended theory
Summary
Scattering amplitudes are traditionally defined from a quantum field theory and the resulting Feynman vertices and Feynman diagrams. We define the theory starting with the usual three-point amplitudes of Einstein gravity1:. There being no polynomial function with the correct spinor and momentum weight These are essentially the unique choice for a three-point amplitude [11] (see Fig. 1). Both shifts change the momenta to be functions of z whilst leaving all momenta null and preserving overall momentum conservation. We need both shifts to construct the S-matrix for the extended theory. Expressions obtained from (11) are not manifestly symmetric as the choice of shift legs breaks crossing symmetry, symmetry is restored in the sum This is a highly non-trivial check that the amplitude has been computed successfully
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