Abstract
We present the derivation of the third subleading order (N3LO) spin-orbit interaction at the state of the art of post-Newtonian (PN) gravity via the EFT of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in sectors with spin, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multi-loop methods. Their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, due to the emergence of dimensional-regularization poles across all loop orders as of the N3LO sectors. At this high order of sectors with spin, it is also critical to extend the formal procedure for the reduction of higher-order time derivatives of spin variables beyond linear order for the first time. This gives rise to a new unique contribution at the present sector. The full interaction potential in Lagrangian form and the general Hamiltonian are provided here for the first time. The consequent gravitational-wave (GW) gauge-invariant observables are also derived, including relations among the binding energy, angular momentum, and emitted frequency. Complete agreement is found between our results, and the binding energy of GW sources, and also with the extrapolated scattering angle in the scattering problem, derived via traditional GR. In contrast with the latter derivation, our framework is free-standing and generic, and has provided theory and results, which have been critical to establish the state of the art, and to push the precision frontier for the measurement of GWs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
LIGO Scientific and Virgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
LIGO Scientific collaboration, Advanced LIGO, Class. Quant. Grav. 32 (2015) 074001 [arXiv:1411.4547] [INSPIRE].
VIRGO collaboration, Advanced Virgo: a second-generation interferometric gravitational wave detector, Class. Quant. Grav. 32 (2015) 024001 [arXiv:1408.3978] [INSPIRE].
LIGO Scientific and Virgo collaborations, GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X 9 (2019) 031040 [arXiv:1811.12907] [INSPIRE].
LIGO Scientific and Virgo collaborations, GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X 11 (2021) 021053 [arXiv:2010.14527] [INSPIRE].
LIGO Scientific et al. collaborations, GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run, arXiv:2111.03606 [INSPIRE].
KAGRA collaboration, Overview of KAGRA: Detector design and construction history, PTEP 2021 (2021) 05A101 [arXiv:2005.05574] [INSPIRE].
L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17 (2014) 2 [arXiv:1310.1528] [INSPIRE].
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].
LIGO Scientific and Virgo collaborations, Tests of general relativity with GW150914, Phys. Rev. Lett. 116 (2016) 221101 [Erratum ibid. 121 (2018) 129902] [arXiv:1602.03841] [INSPIRE].
LIGO Scientific and Virgo collaborations, Properties of the Binary Black Hole Merger GW150914, Phys. Rev. Lett. 116 (2016) 241102 [arXiv:1602.03840] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
LIGO Scientific et al. collaborations, Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences, Astrophys. J. Lett. 915 (2021) L5 [arXiv:2106.15163] [INSPIRE].
LIGO Scientific and Virgo collaborations, Improved analysis of GW150914 using a fully spin-precessing waveform Model, Phys. Rev. X 6 (2016) 041014 [arXiv:1606.01210] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123 (2019) 231104 [arXiv:1909.02375] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders, Phys. Rev. D 102 (2020) 024062 [arXiv:2003.11891] [INSPIRE].
D. Bini et al., Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
J. Blümlein, A. Maier, P. Marquard and G. Schäfer, The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions, Nucl. Phys. B 965 (2021) 115352 [arXiv:2010.13672] [INSPIRE].
L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rept. Prog. Phys. 82 (2019) 016904 [arXiv:1805.10385] [INSPIRE].
A. Antonelli et al., Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios, Phys. Rev. Lett. 125 (2020) 011103 [arXiv:2003.11391] [INSPIRE].
A. Antonelli et al., Gravitational spin-orbit and aligned spin1-spin2 couplings through third-subleading post-Newtonian orders, Phys. Rev. D 102 (2020) 124024 [arXiv:2010.02018] [INSPIRE].
M. Levi and J. Steinhoff, Spinning gravitating objects in the effective field theory in the post-Newtonian scheme, JHEP 09 (2015) 219 [arXiv:1501.04956] [INSPIRE].
M. Levi and J. Steinhoff, Leading order finite size effects with spins for inspiralling compact binaries, JHEP 06 (2015) 059 [arXiv:1410.2601] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 011 [arXiv:1506.05056] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 008 [arXiv:1506.05794] [INSPIRE].
M. Levi and J. Steinhoff, Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order, JCAP 09 (2021) 029 [arXiv:1607.04252] [INSPIRE].
M. Levi and J. Steinhoff, EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity, Class. Quant. Grav. 34 (2017) 244001 [arXiv:1705.06309] [INSPIRE].
M. Levi, S. Mougiakakos and M. Vieira, Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order, JHEP 01 (2021) 036 [arXiv:1912.06276] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational spin-orbit coupling at order G4, JHEP 07 (2021) 115 [arXiv:2003.02827] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational quadratic-in-spin interactions at G4, JHEP 07 (2021) 116 [arXiv:2003.07890] [INSPIRE].
M. Levi and F. Teng, NLO gravitational quartic-in-spin interaction, JHEP 01 (2021) 066 [arXiv:2008.12280] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics, Phys. Lett. B 834 (2022) 137410 [arXiv:2112.01509] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO quadratic-in-spin interactions for generic compact binaries, JHEP 03 (2023) 098 [arXiv:2209.09235] [INSPIRE].
M. Levi, R. Morales and Z. Yin, From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance, arXiv:2210.17538 [INSPIRE].
M. Levi and Z. Yin, Completing the fifth PN precision frontier via the EFT of spinning gravitating objects, JHEP 04 (2023) 079 [arXiv:2211.14018] [INSPIRE].
B.A. Pardo and N.T. Maia, Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach, Phys. Rev. D 102 (2020) 124020 [arXiv:2009.05628] [INSPIRE].
G. Cho, B. Pardo and R.A. Porto, Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order, Phys. Rev. D 104 (2021) 024037 [arXiv:2103.14612] [INSPIRE].
G. Cho, R.A. Porto and Z. Yang, Gravitational radiation from inspiralling compact objects: Spin effects to the fourth post-Newtonian order, Phys. Rev. D 106 (2022) L101501 [arXiv:2201.05138] [INSPIRE].
M. Levi and J. Steinhoff, Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals, JCAP 12 (2014) 003 [arXiv:1408.5762] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995) [INSPIRE].
B. Kol and M. Smolkin, Non-Relativistic Gravitation: From Newton to Einstein and Back, Class. Quant. Grav. 25 (2008) 145011 [arXiv:0712.4116] [INSPIRE].
B. Kol, M. Levi and M. Smolkin, Comparing space+time decompositions in the post-Newtonian limit, Class. Quant. Grav. 28 (2011) 145021 [arXiv:1011.6024] [INSPIRE].
M. Levi, Next to Leading Order gravitational Spin1-Spin2 coupling with Kaluza-Klein reduction, Phys. Rev. D 82 (2010) 064029 [arXiv:0802.1508] [INSPIRE].
M. Levi, Next to Leading Order gravitational Spin-Orbit coupling in an Effective Field Theory approach, Phys. Rev. D 82 (2010) 104004 [arXiv:1006.4139] [INSPIRE].
M. Levi, Effective Field Theories of Post-Newtonian Gravity: A comprehensive review, Rept. Prog. Phys. 83 (2020) 075901 [arXiv:1807.01699] [INSPIRE].
A.J. Hanson and T. Regge, The Relativistic Spherical Top, Annals Phys. 87 (1974) 498 [INSPIRE].
I. Bailey and W. Israel, Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity, Commun. Math. Phys. 42 (1975) 65 [INSPIRE].
K. Yee and M. Bander, Equations of motion for spinning particles in external electromagnetic and gravitational fields, Phys. Rev. D 48 (1993) 2797 [hep-th/9302117] [INSPIRE].
R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc/0511061] [INSPIRE].
M. Levi, Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order, Phys. Rev. D 85 (2012) 064043 [arXiv:1107.4322] [INSPIRE].
J. Hartung and J. Steinhoff, Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries, Annalen Phys. 523 (2011) 783 [arXiv:1104.3079] [INSPIRE].
S. Marsat, A. Bohe, G. Faye and L. Blanchet, Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems, Class. Quant. Grav. 30 (2013) 055007 [arXiv:1210.4143] [INSPIRE].
A. Bohe, S. Marsat, G. Faye and L. Blanchet, Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries, Class. Quant. Grav. 30 (2013) 075017 [arXiv:1212.5520] [INSPIRE].
G. Passarino and M.J.G. Veltman, One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
R.H. Boels, Q. Jin and H. Luo, Efficient integrand reduction for particles with spin, arXiv:1802.06761 [INSPIRE].
L. Chen, A prescription for projectors to compute helicity amplitudes in D dimensions, Eur. Phys. J. C 81 (2021) 417 [arXiv:1904.00705] [INSPIRE].
V.A. Smirnov, Feynman integral calculus, Springer, Berlin, Heidelberg (2006) [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
T. Damour and G. Schaefer, Higher Order Relativistic Periastron Advances and Binary Pulsars, Nuovo Cim. B 101 (1988) 127 [INSPIRE].
Acknowledgments
J-WK was supported by the Science and Technology Facilities Council (STFC) Consolidated Grant ST/T000686/1 “Amplitudes, Strings and Duality”. ML has been supported by the STFC Rutherford Grant ST/V003895 “Harnessing QFT for Gravity” and by the Mathematical Institute University of Oxford. ZY is supported by the Knut and Alice Wallenberg Foundation under grants KAW 2018.0116 and KAW 2018.0162.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.14949
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kim, JW., Levi, M. & Yin, Z. N3LO spin-orbit interaction via the EFT of spinning gravitating objects. J. High Energ. Phys. 2023, 184 (2023). https://doi.org/10.1007/JHEP05(2023)184
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)184