On higher-derivative effects on the gravitational potential and particle bending. (English) Zbl 1434.83033
Summary: 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 \(R^3\) 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 \(\Phi R^2,\) 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.
MSC:
| 83C45 | Quantization of the gravitational field |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 83E30 | String and superstring theories in gravitational theory |
| 81V73 | Bosonic systems in quantum theory |
Software:
LiteRedReferences:
| [1] | Bern, Zvi; Dixon, Lance; Dunbar, David C.; Kosower, David A., One-loop n-point gauge theory amplitudes, unitarity and collinear limits, Nuclear Physics B, 425, 1-2, 217-260 (1994) · Zbl 1049.81644 · doi:10.1016/0550-3213(94)90179-1 |
| [2] | Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys.B 435 (1995) 59 [hep-ph/9409265] [INSPIRE]. · Zbl 1049.81644 |
| [3] | Neill, D.; Rothstein, Iz, Classical Space-Times from the S Matrix, Nucl. Phys., B 877, 177 (2013) · Zbl 1284.83052 · doi:10.1016/j.nuclphysb.2013.09.007 |
| [4] | Bjerrum-Bohr, Nej; Donoghue, Jf; Vanhove, P., On-shell Techniques and Universal Results in Quantum Gravity, JHEP, 02, 111 (2014) · Zbl 1333.83043 · doi:10.1007/JHEP02(2014)111 |
| [5] | 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.D 67 (2003) 084033 [Erratum ibid.D 71 (2005) 069903][hep-th/0211072] [INSPIRE]. |
| [6] | Khriplovich, I. B.; Kirilin, G. G., Quantum long-range interactions in general relativity, Journal of Experimental and Theoretical Physics, 98, 6, 1063-1072 (2004) · Zbl 1097.83516 · doi:10.1134/1.1777618 |
| [7] | Y. Iwasaki, Quantum theory of gravitation vs. classical theory: fourth-order potential, Frog. Theor. Phys.46 (1971) 1587 [INSPIRE]. |
| [8] | Bjerrum-Bohr, Nej; Donoghue, Jf; Holstein, Br; Planté, L.; Vanhove, P., Bending of Light in Quantum Gravity, Phys. Rev. Lett., 114, 061301 (2015) · doi:10.1103/PhysRevLett.114.061301 |
| [9] | Bjerrum-Bohr, Nej; Donoghue, Jf; Holstein, Br; Planté, L.; Vanhove, P., Light-like Scattering in Quantum Gravity, JHEP, 11, 117 (2016) · Zbl 1390.83057 · doi:10.1007/JHEP11(2016)117 |
| [10] | D. Bai and Y. Huang, More on the Bending of Light in Quantum Gravity, Phys. Rev.D 95 (2017) 064045 [arXiv:1612 . 07629] [INSPIRE]. |
| [11] | H.-H. Chi, Graviton Bending in Quantum Gravity from One-Loop Amplitudes, Phys. Rev.D 99 (2019) 126008 [arXiv:1903. 07944] [INSPIRE]. |
| [12] | Luna, A.; Monteiro, R.; Nicholson, I.; O’Connell, D.; White, Cd, The double copy: Bremsstrahlung and accelerating black holes, JHEP, 06, 023 (2016) · Zbl 1388.83025 · doi:10.1007/JHEP06(2016)023 |
| [13] | F. Cachazo and A. Guevara, Leading Singularities and Classical Gravitational Scattering,arXiv:1705.10262 [INSPIRE]. · Zbl 1435.83076 |
| [14] | Bjerrum-Bohr, Nej; Damgaard, Ph; Festuccia, G.; Plante, L.; Vanhove, P., General Relativity from Scattering Amplitudes, Phys. Rev. Lett., 121, 171601 (2018) · doi:10.1103/PhysRevLett.121.171601 |
| [15] | Plefka, J.; Steinhoff, J.; Wormsbecher, W., Effective action of dilaton gravity as the classical double copy of Yang-Mills theory, Phys. Rev., D 99, 024021 (2019) |
| [16] | Cheung, C.; Rothstein, Iz; Solon, Mp, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett., 121, 251101 (2018) · doi:10.1103/PhysRevLett.121.251101 |
| [17] | Kosower, Da; Maybee, B.; O’Connell, D., Amplitudes, Observables and Classical Scattering, JHEP, 02, 137 (2019) · Zbl 1411.81217 · doi:10.1007/JHEP02(2019)137 |
| [18] | Guevara, A.; Ochirov, A.; Vines, J., Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP, 09, 056 (2019) · Zbl 1423.83030 · doi:10.1007/JHEP09(2019)056 |
| [19] | Bern, Z.; Cheung, C.; Roiban, R.; Shen, C-H; Solon, Mp; Zeng, M., Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett., 122, 201603 (2019) · doi:10.1103/PhysRevLett.122.201603 |
| [20] | Y.F. Bautista and A. Guevara, From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems,arXiv:1903.12419 [INSPIRE]. |
| [21] | A. Koemans Collado, P. Di Vecchia and R. Russo, Revisiting the second post-Minkowskian eikona l and the dynamics of binary black holes, Phys. Rev.D 100 (2019) 066028 [arXiv:1904.02667] [INSPIRE]. |
| [22] | J.F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev.D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE]. |
| [23] | Goldberger, Wd; Rothstein, Iz, An Effective field theory of gravity for extended objects, Phys. Rev., D 73, 104029 (2006) |
| [24] | Holstein, Br; Donoghue, Jf, Classical physics and quantum loops, Phys. Rev. Lett., 93, 201602 (2004) · doi:10.1103/PhysRevLett.93.201602 |
| [25] | Damour, T.; Schäfer, G., Lagrangians forn point masses at the second post-Newtonian approximation of general relativity, Gen. Rel. Grav., 17, 879 (1985) · Zbl 0568.70014 · doi:10.1007/BF00773685 |
| [26] | Gilmore, Jb; Ross, A., Effective field theory calculation of second post-Newtonian binary dynamics, Phys. Rev., D 78, 124021 (2008) |
| [27] | Damour, Thibault; Jaranowski, Piotr; Schäfer, Gerhard, Dimensional regularization of the gravitational interaction of point masses, Physics Letters B, 513, 1-2, 147-155 (2001) · Zbl 0969.83506 · doi:10.1016/S0370-2693(01)00642-6 |
| [28] | L. Blanchet, T. Damour and G. Esposito-Farese, Dimensional regularization of the third postNewtonian dynamics of point particles in harmonic coordinates, Phys. Rev.D 69 (2004) 124007 [gr-qc/0311052] [INSPIRE]. |
| [29] | Y. Itoh and T. Futamase, New derivation of a third postNewtonian equation of motion for relativistic compact binaries without ambiguity, Phys. Rev.D 68 (2003) 121501 [gr-qc/0310028] [INSPIRE]. |
| [30] | S. Foffa and R. Sturani, Effective field theory calculation of conservative binary dynamics at third post-Newtonian order, Phys. Rev.D 84 (2011) 044031 [arXiv:1104.1122] [INSPIRE]. |
| [31] | P. Jaranowski and G. Schäfer, Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems, Phys. Rev.D 86 (2012) 061503 [arXiv:1207.5448] [INSPIRE]. |
| [32] | T. Damour, P. Jaranowski and G. Schäfer, No nlocal-i n-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev.D 89 (2014) 064058 [arXiv:1401.4548] [INSPIRE]. |
| [33] | T. Damour, P. Jaranowski and G. Schäfer, Fourth post-Newtonian effective one-body dynamics, Phys. Rev.D 91 (2015) 084024 [arXiv:1502.07245] [INSPIRE]. |
| [34] | T. Damour, P. Jaranowski and G. Schäfer, Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity, Phys. Rev.D 93 (2016) 084014 [arXiv:1601.01283] [INSPIRE]. |
| [35] | L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation, Phys. Rev.D 93 (2016) 084037 [arXiv:1512.02876] [INSPIRE]. |
| [36] | L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order, Phys. Rev.D 95 (2017) 044026 [arXiv:1610.07934] [INSPIRE]. |
| [37] | S. Foffa and R. Sturani, Dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant, Phys. Rev.D 87 (2013) 064011 [arXiv:1206.7087] [INSPIRE]. |
| [38] | Foffa, S.; Mastrolia, P.; Sturani, R.; Sturm, C., Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant, Phys. Rev., D 95, 104009 (2017) |
| [39] | Foffa, S.; Mastrolia, P.; Sturani, R.; Sturm, C.; Torres Bobadilla, Wj, Static two-body potential at fifth post-Newtonian order, Phys. Rev. Lett., 122, 241605 (2019) · doi:10.1103/PhysRevLett.122.241605 |
| [40] | Blumlein, J.; Maier, A.; Marquard, P., Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses, Phys. Lett., B 800, 135100 (2020) · doi:10.1016/j.physletb.2019.135100 |
| [41] | Einstein, A.; Infeld, L.; Hoffmann, B., The Gravitational equations and the problem of motion, Annals Math., 39, 65 (1938) · JFM 64.0769.01 · doi:10.2307/1968714 |
| [42] | A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev.D 59 (1999) 084006 [gr-qc/9811091] [INSPIRE]. |
| [43] | Damour, T., Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev., D 94, 104015 (2016) |
| [44] | T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev.D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE]. |
| [45] | Van Nieuwenhuizen, P.; Wu, Cc, On Integral Relations for Invariants Constructed from Three Riemann Tensors and their Applications in Quantum Gravity, J. Math. Phys., 18, 182 (1977) · doi:10.1063/1.523128 |
| [46] | Broedel, J.; Dixon, Lj, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP, 10, 091 (2012) · doi:10.1007/JHEP10(2012)091 |
| [47] | Kawai, H.; Lewellen, Dc; Tye, Shh, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys., B 269, 1 (1986) · doi:10.1016/0550-3213(86)90362-7 |
| [48] | Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev.D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE]. |
| [49] | Emond, Wt; Moynihan, N., Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity, JHEP, 12, 019 (2019) · Zbl 1431.83048 · doi:10.1007/JHEP12(2019)019 |
| [50] | Metsaev, Rr; Tseytlin, Aa, Curvature Cubed Terms in String Theory Effective Actions, Phys. Lett., B 185, 52 (1987) · doi:10.1016/0370-2693(87)91527-9 |
| [51] | Bjerrum-Bohr, Nej, String theory and the mapping of gravity into gauge theory, Phys. Lett., B 560, 98 (2003) · Zbl 1059.81145 · doi:10.1016/S0370-2693(03)00373-3 |
| [52] | M. Accettulli Huber, A. Brandhuber, S. DeAngelis and G. Travaglini, A note on the absence of R^2corrections to Newton’s potential,arXiv:1911.10108 [INSPIRE]. |
| [53] | Tseytlin, Aa, Ambiguity in the Effective Action in String Theories, Phys. Lett., B 176, 92 (1986) · doi:10.1016/0370-2693(86)90930-5 |
| [54] | 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]. |
| [55] | S. Deser and A.N. Redlich, String Induced Gravity and Ghost Freedom, Phys. Lett.B 176 (1986) 350 [Erratum ibid.B 186 (1987) 461] [INSPIRE]. |
| [56] | Julve, J.; Tonin, M., Quantum Gravity with Higher Derivative Terms, Nuovo Cim., B 46, 137 (1978) · doi:10.1007/BF02748637 |
| [57] | Álvarez-Gaumé, L.; Kehagias, A.; Kounnas, C.; Lust, D.; Riotto, A., Aspects of Quadratic Gravity, Fortsch. Phys., 64, 176 (2016) · Zbl 1339.83058 · doi:10.1002/prop.201500100 |
| [58] | Simon, Jz, Higher Derivative Lagrangians, Nonlocality, Problems and Solutions, Phys. Rev., D 41, 3720 (1990) |
| [59] | Simon, Jz, The Stability of fiat space, semiclassical gravity and higher d erivativ es, Phys. Rev., D 43, 3308 (1991) |
| [60] | Camanho, Xo; Edelstein, Jd; Maldacena, J.; Zhiboedov, A., Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP, 02, 020 (2016) · Zbl 1388.83093 · doi:10.1007/JHEP02(2016)020 |
| [61] | Bern, Z.; Dixon, Lj; Perelstein, M.; Rozowsky, Js, Multileg one loop gravity amplitudes from gauge theory, Nucl. Phys., B 546, 423 (1999) · Zbl 0953.83006 · doi:10.1016/S0550-3213(99)00029-2 |
| [62] | B.R. Holstein and A. Ross, Spin Effects in Long Range Gravitational Scattering,arXiv:0802.0716 [INSPIRE]. |
| [63] | R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction,arXiv:1212.2685 [INSPIRE]. |
| [64] | R.N. Lee, LiteRed 1.4 : a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser.523 (2014) 012059 [arXiv:1310.1145] [INSPIRE]. |
| [65] | Donoghue, Jf; Holstein, Br, Quantum Mechanics in Curved Space, Am. J. Phys., 54, 827 (1986) · doi:10.1119/1.14423 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
