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.

arXiv comment23 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 (41)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Effective one-body approach to general relativistic two-body dynamics
• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Amplitudes, Observables, and Classical Scattering
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• High-energy gravitational scattering and the general relativistic two-body problem
• Dimensional regularization of the gravitational interaction of point masses
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Classical Space-Times from the S Matrix
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• On-shell Techniques and Universal Results in Quantum Gravity
• The double copy: Bremsstrahlung and accelerating black holes
• Aspects of Quadratic Gravity
• Fourth post-Newtonian effective one-body dynamics
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Bending of Light in Quantum Gravity
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• Classical Physics and Quantum Loops
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Light-like Scattering in Quantum Gravity
• 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
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Quantum long-range interactions in general relativity
• String theory and the mapping of gravity into gauge theory
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• More on the Bending of Light in Quantum Gravity
• Graviton Bending in Quantum Gravity from One-Loop Amplitudes

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• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• A worldsheet for Kerr
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Black-hole ringdown as a probe of higher-curvature gravity theories
• Tidal effects in quantum field theory
• A new gauge-invariant double copy for heavy-mass effective theory
• Classical Solutions and their Double Copy in Split Signature
• Mining the Geodesic Equation for Scattering Data
• Resummed spinning waveforms from five-point amplitudes
• Causality Constraints on Gravitational Effective Field Theories
• Classical Yang-Mills observables from amplitudes
• On the Double Copy for Spinning Matter
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• The Double Copy of Massive Scalar-QCD
• Rotating Black Holes in Cubic Gravity
• Amplitude bases in generic EFTs
• Large Gauge Effects and the Structure of Amplitudes
• Running Love Numbers and the Effective Field Theory of Gravity
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Causality and quasi-normal modes in the GREFT
• A scattering amplitudes approach to hard thermal loops
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Wave scattering event shapes at high energies
• Visions in Quantum Gravity
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation
• Waveforms from Amplitudes
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity
• Classical gravitational scattering from a gauge-invariant double copy
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• The Radial Action from Probe Amplitudes to All Orders