Abstract
We derive the third subleading (N3LO) corrections of the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (PN) gravity. These corrections consist of contributions from 4 sectors for generic compact binaries, that enter at the fifth PN order. One of these contributions is due to a new tidal interaction, that is unique to the sectors with spin, and complements the first tidal interaction that also enters at this PN order in the simple point-mass sector. The evaluation of Feynman graphs is carried out in a generic dimension via advanced multi-loop methods, and gives rise to dimensional-regularization poles in conjunction with logarithms. At these higher-spin sectors the reduction of generalized Lagrangians entails redefinitions of the position beyond linear order. We provide here the most general Lagrangians and Hamiltonians. We then specify the latter to simplified configurations, and derive the consequent gauge-invariant relations among the binding energy, angular momentum, and frequency. We end with a derivation of all the scattering angles that correspond to an extension of our Hamiltonians to the scattering problem in the simplified aligned-spins configuration, as a guide to scattering-amplitudes studies.
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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].
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, 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, Virgo and KAGRA collaborations, GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run, arXiv:2111.03606 [INSPIRE].
LIGO Scientific and Virgo collaborations, Tests of general relativity with GW150914, Phys. Rev. Lett. 116 (2016) 221101 [arXiv:1602.03841] [Erratum ibid. 121 (2018) 129902] [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, Improved analysis of GW150914 using a fully spin-precessing waveform Model, Phys. Rev. X 6 (2016) 041014 [arXiv:1606.01210] [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, KAGRA and Virgo collaborations, Observation of Gravitational Waves from Two Neutron Star-Black Hole Coalescences, Astrophys. J. Lett. 915 (2021) L5 [arXiv:2106.15163] [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].
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].
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, T. Damour, A. Geralico, S. Laporta and P. Mastrolia, Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [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].
A. Antonelli, C. Kavanagh, M. Khalil, J. Steinhoff and J. Vines, 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, C. Kavanagh, M. Khalil, J. Steinhoff and J. Vines, 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, A.J. Mcleod and M. Von Hippel, N3LO gravitational spin-orbit coupling at order G4, JHEP 07 (2021) 115 [arXiv:2003.02827] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects, arXiv:2208.14949 [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.K. Mandal, P. Mastrolia, R. Patil and J. Steinhoff, Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework, arXiv:2209.00611 [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, 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].
B.M. Barker and R.F. O’Connell, Gravitational Two-Body Problem with Arbitrary Masses, Spins, and Quadrupole Moments, Phys. Rev. D 12 (1975) 329 [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, Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order, Phys. Rev. D 85 (2012) 064043 [arXiv:1107.4322] [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].
T. Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677 (2008) 1216 [arXiv:0711.2420] [INSPIRE].
T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80 (2009) 084035 [arXiv:0906.0096] [INSPIRE].
T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80 (2009) 084018 [arXiv:0906.1366] [INSPIRE].
B. Kol and M. Smolkin, Black hole stereotyping: Induced gravito-static polarization, JHEP 02 (2012) 010 [arXiv:1110.3764] [INSPIRE].
A. Le Tiec and M. Casals, Spinning Black Holes Fall in Love, Phys. Rev. Lett. 126 (2021) 131102 [arXiv:2007.00214] [INSPIRE].
A. Le Tiec, M. Casals and E. Franzin, Tidal Love Numbers of Kerr Black Holes, Phys. Rev. D 103 (2021) 084021 [arXiv:2010.15795] [INSPIRE].
H.S. Chia, Tidal deformation and dissipation of rotating black holes, Phys. Rev. D 104 (2021) 024013 [arXiv:2010.07300] [INSPIRE].
P. Charalambous, S. Dubovsky and M.M. Ivanov, On the Vanishing of Love Numbers for Kerr Black Holes, JHEP 05 (2021) 038 [arXiv:2102.08917] [INSPIRE].
P. Charalambous, S. Dubovsky and M.M. Ivanov, Hidden Symmetry of Vanishing Love Numbers, Phys. Rev. Lett. 127 (2021) 101101 [arXiv:2103.01234] [INSPIRE].
G. Castro, L. Gualtieri and P. Pani, Hidden symmetry between rotational tidal Love numbers of spinning neutron stars, Phys. Rev. D 104 (2021) 044052 [arXiv:2103.16595] [INSPIRE].
L. Blanchet and G. Faye, General relativistic dynamics of compact binaries at the third postNewtonian order, Phys. Rev. D 63 (2001) 062005 [gr-qc/0007051] [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].
M. Levi, Effective Field Theories of Post-Newtonian Gravity: A comprehensive review, Rept. Prog. Phys. 83 (2020) 075901 [arXiv:1807.01699] [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. 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 and F. Teng, NLO gravitational quartic-in-spin interaction, JHEP 01 (2021) 066 [arXiv:2008.12280] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995).
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].
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 and Z. Yin, Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects, arXiv:2211.14018 [INSPIRE].
J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
V.A. Smirnov, Feynman integral calculus, Springer, Berlin, Germany (2006).
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [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].
L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rept. Prog. Phys. 82 (2019) 016904 [arXiv:1805.10385] [INSPIRE].
A. Edison and M. Levi, A tale of tails through generalized unitarity, Phys. Lett. B 837 (2023) 137634 [arXiv:2202.04674] [INSPIRE].
T. Damour and G. Schaefer, Higher Order Relativistic Periastron Advances and Binary Pulsars, Nuovo Cim. B 101 (1988) 127 [INSPIRE].
D. Kosmopoulos and A. Luna, Quadratic-in-spin Hamiltonian at \( \mathcal{O} \)(G2) from scattering amplitudes, JHEP 07 (2021) 037 [arXiv:2102.10137] [INSPIRE].
Z. Liu, R.A. Porto and Z. Yang, Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics, JHEP 06 (2021) 012 [arXiv:2102.10059] [INSPIRE].
G.U. Jakobsen and G. Mogull, Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory, Phys. Rev. Lett. 128 (2022) 141102 [arXiv:2201.07778] [INSPIRE].
M. Levi, What is love? New physics at the state of the art with spins, Kavli Institute for Theoretical Physics Audiovisual, https://doi.org/10.26081/K6N349 (2022).
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Kim, JW., Levi, M. & Yin, Z. N3LO quadratic-in-spin interactions for generic compact binaries. J. High Energ. Phys. 2023, 98 (2023). https://doi.org/10.1007/JHEP03(2023)098
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DOI: https://doi.org/10.1007/JHEP03(2023)098