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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.
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T. Damour, P. Jaranowski, and G. Schäfer, “Dimensional regularization of the gravitational interaction of point masses,” Phys. Lett
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Y. Itoh and T. Futamase, “New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity,” Phys. Rev
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L. Blanchet, T. Damour, and G. Esposito-Farese, “Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates,” Phys. Rev
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N. E. J. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, “Quantum gravitational corrections to the nonrelativistic scattering potential of two masses,” Phys. Rev
2005
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D. Bai and Y. Huang, “More on the Bending of Light in Quantum Gravity,” Phys. Rev
2017
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