On higher-derivative effects on the gravitational potential and particle bending
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Springer
Received: June 18, Revised: November 4, Accepted: December 5, Published: January 2,
2019 2019 2019 2020
Andreas Brandhuber and Gabriele Travaglini Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
E-mail: [email protected], [email protected] Abstract: Using modern amplitude techniques we compute the leading classical and quantum corrections to the gravitational potential between two massive scalars induced by adding cubic terms to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same R3 deformations, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude. Similarly to the Einstein-Hilbert case, we find that the classical contribution to the bending angle is universal, but unlike that case, universality is preserved also by the first quantum correction. Finally we extend our analysis to include a deformation of the form ΦR2 , where Φ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the R3 term, and compute its effect on the graviton bending. Keywords: Scattering Amplitudes, Effective Field Theories, Models of Quantum Gravity ArXiv ePrint: 1905.05657
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)010
JHEP01(2020)010
On higher-derivative effects on the gravitational potential and particle bending
Contents 1 Introduction
1
2 R3 corrections to the gravitational potential
4 9 10 10 12 13 14
4 Closing comments
16
A Integrals and Fourier transforms
17
1
Introduction
Modern on-shell methods [1, 2] have proven extremely successful for the efficient computation of scattering amplitudes in gauge theory and gravity. By working with on-shell quantities one performs computations which are at every stage gauge invariant, yielding considerable conceptual and practical advantages. Recently, amplitude methods have been applied to the computation of post-Newtonian and post-Minkowskian corrections in General Relativity (GR). Examples include the computation of the leading classical [3, 4] and quantum [4] corrections at O(G2N ) to the Newton potential, confirming the earlier result of [5–7] based on Feynman diagrams, as well as the computation of the particle bending angle [8–11] (for other recent related computations see [12–21]). This is clearly a timely endeavour as LIGO necessitates computations in GR of unprecedented precision. Feynman diagram calculations have been employed for many years to extract relevant quantities for astrophysical processes. In this context, gravity is treated as an effective field theory [22], making it perfectly sensible to compute quantum corrections even if the theory is non-renormalisable. An alternative, systematic effective field theory treatment was introduced in [23], where the massive objects are treated as classical sources. The main focus fo
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