Abstract
We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects of the potential, including some non-dispersive terms that lead to black hole solutions (including quantum corrections) that agree with those derived in Einsteinian cubic gravity (ECG). We show that these non-dispersive terms could be obtained from theories that include the Gauss- Bonnet cubic invariant G3. In addition, we derive the one-loop scattering amplitudes using both unitarity cuts and via the leading singularity, showing that the classical effects of higher derivative gravity can be easily obtained directly from the leading singularity with far less computational cost.
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References
J. Bedford, A. Brandhuber, B.J. Spence and G. Travaglini, A Recursion relation for gravity amplitudes, Nucl. Phys.B 721 (2005) 98 [hep-th/0502146] [INSPIRE].
D. Nguyen, M. Spradlin, A. Volovich and C. Wen, The Tree Formula for MHV Graviton Amplitudes, JHEP07 (2010) 045 [arXiv:0907.2276] [INSPIRE].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming Tree Amplitudes In General Relativity, JHEP11 (2007) 057 [hep-th/0702032] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, G. Festuccia, L. Planté and P. Vanhove, General Relativity from Scattering Amplitudes, Phys. Rev. Lett.121 (2018) 171601 [arXiv:1806.04920] [INSPIRE].
H. Johansson and J. Nohle, Conformal Gravity from Gauge Theory, arXiv:1707.02965 [INSPIRE].
S. He and Y. Zhang, New Formulas for Amplitudes from Higher-Dimensional Operators, JHEP02 (2017) 019 [arXiv:1608.08448] [INSPIRE].
D.C. Dunbar, J.H. Godwin, G.R. Jehu and W.B. Perkins, Diagrammar in an Extended Theory of Gravity, Phys. Lett.B 771 (2017) 230 [arXiv:1702.08273] [INSPIRE].
D.C. Dunbar, J.H. Godwin, G.R. Jehu and W.B. Perkins, Loop Amplitudes in an Extended Gravity Theory, Phys. Lett.B 780 (2018) 41 [arXiv:1711.05526] [INSPIRE].
R. Carballo-Rubio, F. Di Filippo and N. Moynihan, Taming higher-derivative interactions and bootstrapping gravity with soft theorems, JCAP10 (2019) 030 [arXiv:1811.08192] [INSPIRE].
C. Cheung, I.Z. Rothstein and M.P. Solon, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett.121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett.122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
T. Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev.D 94 (2016) 104015 [arXiv:1609.00354] [INSPIRE].
T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev.D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE].
P. Bueno and P.A. Cano, Four-dimensional black holes in Einsteinian cubic gravity, Phys. Rev.D 94 (2016) 124051 [arXiv:1610.08019] [INSPIRE].
A.A. Tseytlin, Vector Field Effective Action in the Open Superstring Theory, Nucl. Phys.B 276 (1986) 391 [Erratum ibid.B 291 (1987) 876] [INSPIRE].
P. Bueno and P.A. Cano, Einsteinian cubic gravity, Phys. Rev.D 94 (2016) 104005 [arXiv:1607.06463] [INSPIRE].
I. Güllü, T.C. Sisman and B. Tekin, Born-Infeld Gravity with a Massless Graviton in Four Dimensions, Phys. Rev.D 91 (2015) 044007 [arXiv:1410.8033] [INSPIRE].
F. Cachazo and A. Guevara, Leading Singularities and Classical Gravitational Scattering, arXiv:1705.10262 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Curvature Cubed Terms in String Theory Effective Actions, Phys. Lett.B 185 (1987) 52 [INSPIRE].
J. Broedel and L.J. Dixon, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP10 (2012) 091 [arXiv:1208.0876] [INSPIRE].
K.A. Kazakov, On the notion of potential in quantum gravity, Phys. Rev.D 63 (2001) 044004 [hep-th/0009220] [INSPIRE].
Y. Iwasaki, Fourth-order gravitational potential based on quantum field theory, Lett. Nuovo Cim.1 (1971) 783 [INSPIRE].
Y. Iwasaki, Quantum Theory of Gravitation vs. Classical Theory: Fourth-Order Potential, Prog. Theor. Phys.46 (1971) 1587 [INSPIRE].
M.J. Duff, Quantum corrections to the Schwarzschild solution, Phys. Rev.D 9 (1974) 1837 [INSPIRE].
D. Neill and I.Z. Rothstein, Classical Space-Times from the S Matrix, Nucl. Phys.B 877 (2013) 177 [arXiv:1304.7263] [INSPIRE].
G. Modanese, Potential energy in quantum gravity, Nucl. Phys.B 434 (1995) 697 [hep-th/9408103] [INSPIRE].
B.R. Holstein and J.F. Donoghue, Classical physics and quantum loops, Phys. Rev. Lett.93 (2004) 201602 [hep-th/0405239] [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev.D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables and Classical Scattering, JHEP02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun.197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys.B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
A. Guevara, Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, JHEP04 (2019) 033 [arXiv:1706.02314] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
Y.F. Bautista and A. Guevara, From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems, arXiv:1903.12419 [INSPIRE].
J.F. Donoghue, Dispersion relations and effective field theory, in proceedings of the Advanced School on Effective Theories, Almunecar, Spain, 25 June–1 July 1995, hep-ph/9607351 [INSPIRE].
B.R. Holstein and A. Ross, Spin Effects in Long Range Gravitational Scattering, arXiv:0802.0716 [INSPIRE].
A. Brandhuber and G. Travaglini, On higher-derivative effects on the gravitational potential and particle bending, arXiv:1905.05657 [INSPIRE].
R.A. Hennigar and R.B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev.D 95 (2017) 064055 [arXiv:1610.06675] [INSPIRE].
J.M. Martin-Garcia, R. Portugal and L.R.U. Manssur, The Invar Tensor Package, Comput. Phys. Commun.177 (2007) 640 [arXiv:0704.1756] [INSPIRE].
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Emond, W.T., Moynihan, N. Scattering amplitudes, black holes and leading singularities in cubic theories of gravity. J. High Energ. Phys. 2019, 19 (2019). https://doi.org/10.1007/JHEP12(2019)019
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DOI: https://doi.org/10.1007/JHEP12(2019)019