Abstract
Using the CHY-formalism and its extension to a double cover we provide covariant expressions for tree-level amplitudes with two massive scalar legs and an arbitrary number of gravitons in D dimensions. Using unitarity methods, such amplitudes are needed inputs for the computation of post-Newtonian and post-Minkowskian expansions in classical general relativity.
Highlights
From a practical point of view, it suffices to evaluate amplitudes with two scalar legs and (n + 1) gluons and subsequently turning them into scalar-graviton amplitudes by KLT-squaring
One key point of the present calculation is the computation of a factorized expression for the amplitudes of two massive scalars coupled to Yang-Mills theory, expressing them as sums over lower-point amplitudes which are combinations of scalar-gluon amplitudes and pure gluon amplitudes
We have presented different methods to compute the tree-level scattering amplitudes of two massive scalars and an in principle arbitrary number of gravitons in D-dimensions
Summary
We first present a simple way to obtain explicit expressions for the scattering amplitudes of two massive scalars and n gluons. Since our method is based on the CHY approach, we give a very brief review of this formalism. We apply the factorization method developed in [43] to obtain, up to six-point, analytical expressions for the scattering of gluons where two of them, suitably defined, are massive. We turn the two massive gluons into massive scalars, providing the scattering amplitudes for two massive scalars and in principle any number of massless gluons
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