On higher-derivative effects on the gravitational potential and particle bending

Abstract

Using modern amplitude techniques we compute the leading classical and quantum corrections to the classical gravitational potential between two massive scalars induced by adding an $R^3$ term to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same $R^3$ deformation, 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 $\Phi R^2$, where $\Phi$ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the $R^3$ term, and compute its effect on the graviton bending.

23 pages, 4 figures. v2: typos corrected, one reference added, several comments and clarifications added in Section 2. v3: JHEP version. v4: typos corrected

References in corpus (11)

• New Relations for Gauge-Theory Amplitudes
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Fourth post-Newtonian effective one-body dynamics
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Static two-body potential at fifth post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• Graviton Bending in Quantum Gravity from One-Loop Amplitudes

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