Abstract

We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin- $$ \frac{1}{2} $$ , spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum ℏ dependent terms using the same eikonal method.

Highlights

  • This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude

  • In this paper we focus on providing further details on the effective field theory computation of light-like scattering in quantum gravity

  • While we have found universality and agreement with general relativity for the classical physics component of the result, i.e., the so called post-Newtonian corrections, field theory has produced a new type of contribution of quantum origin, which has no precedence in classical general relativity

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Summary

General relativity as an effective field theory and one-loop amplitudes

Including gravitational interactions in particle physics models is a straightforward exercise employing ideas from effective field theory. [35,36,37,38]) can be adapted to gravity [39, 40] using the Kawai-Lewellen-Tye (KLT) string theory relations [41, 42] Using these methods, the only required input for effective field theory computations is that of compact on-shell tree amplitudes, since loop amplitudes can be written in terms of trees by the use of unitarity as the central consistency requirement. The only required input for effective field theory computations is that of compact on-shell tree amplitudes, since loop amplitudes can be written in terms of trees by the use of unitarity as the central consistency requirement To illustrate how this program is carried out in practice, we follow the procedure outlined in ref. The consequence of the monodromy BCJ relations for one-loop integral coefficients have been studied in [45] and [46], while a string theory based systematic derivation of these relations was given in [47]

The one-loop integral coefficients
The low energy limit of the cut constructible one-loop amplitude
Bending formula from general relativity
Leading Newtonian correction
Bending via the eikonal approximation
15 G2NM 2π 4 b2
Bending via geometrical optics
Discussion
Helicity formalism conventions
The gravitational Compton amplitudes
The one-graviton tree-level amplitudes
B Integrals
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