Built on

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
Original
1901
Earlier work this paper cites.
S. Foffa, R. A. Porto, I. Rothstein, and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian,” Phys. Rev. D
Original
1903
Earlier work this paper cites.
W. Cho and K. Lee, “Heterotic Kerr-Schild Double Field Theory and Classical Double Copy,” JHEP
Original
1904
Earlier work this paper cites.
W. T. Emond and N. Moynihan, “Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity,” JHEP
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, “Post-Minkowskian Hamiltonians in general relativity,” Phys. Rev. D
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell, and J. Vines, “Observables and amplitudes for spinning particles and black holes,” JHEP
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y.-t. Huang, and D. O’Connell, “Kerr black holes as elementary particles,” JHEP
Original
1906
Earlier work this paper cites.
H. Johansson and A. Ochirov, “Double copy for massive quantum particles with spin,” JHEP
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov, and J. Vines, “Black-hole scattering with general spin directions from minimal-coupling amplitudes,” Phys. Rev. D
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP
Original
1908
Earlier work this paper cites.
H. Godazgar, M. Godazgar, and C. Pope, “Taub-NUT from the Dirac monopole,” Phys. Lett. B
Original
1908
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The Duality Between Color and Kinematics and its Applications,” arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
N. Siemonsen and J. Vines, “Test black holes, scattering amplitudes and perturbations of Kerr spacetime,” Phys. Rev. D
Original
1909
Earlier work this paper cites.
N. Moynihan, “Kerr-Newman from Minimal Coupling,” JHEP
Original
1909
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” JHEP
Original
1910
Earlier work this paper cites.
I. Bah, R. Dempsey, and P. Weck, “Kerr-Schild Double Copy and Complex Worldlines,” JHEP
Original
1910
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist),” JHEP
Original
1911
Earlier work this paper cites.
R. Alawadhi, D. S. Berman, B. Spence, and D. Peinador Veiga, “S-duality and the double copy,” JHEP
Original
1911
Earlier work this paper cites.
Y.-T. Huang, U. Kol, and D. O’Connell, “Double copy of electric-magnetic duality,” Phys. Rev. D
Original
1911
Earlier work this paper cites.
W. D. Goldberger and J. Li, “Strings, extended objects, and the classical double copy,” JHEP
Original
1912
Earlier work this paper cites.
E. T. Newman and A. I. Janis, “Note on the Kerr spinning particle metric,” J. Math. Phys
1965
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B
1986
Earlier work this paper cites.
J. F. Donoghue, “Leading quantum correction to the Newtonian potential,” Phys. Rev. Lett
1994
Earlier work this paper cites.
J. F. Donoghue, “General relativity as an effective field theory: The leading quantum corrections,” Phys. Rev. D
1994
Earlier work this paper cites.
J. F. Donoghue and T. Torma, “On the power counting of loop diagrams in general relativity,” Phys. Rev. D
1996
Earlier work this paper cites.
Wiley, 1998
Original
J. D. Jackson, Classical Electrodynamics · 1998
Earlier work this paper cites.
A. Buonanno and T. Damour, “Effective one-body approach to general relativistic two-body dynamics,” Phys. Rev. D
1999
Earlier work this paper cites.
A. Buonanno and T. Damour, “Transition from inspiral to plunge in binary black hole coalescences,” Phys. Rev. D
2000
Earlier work this paper cites.
T. Damour, P. Jaranowski, and G. Schaefer, “On the determination of the last stable orbit for circular general relativistic binaries at the third postNewtonian approximation,” Phys. Rev. D
2000
Earlier work this paper cites.
T. Damour, “Coalescence of two spinning black holes: an effective one-body approach,” Phys. Rev. D
2001
Earlier work this paper cites.
Z. Bern, H. Ita, J. Parra-Martinez, and M. S. Ruf, “Universality in the classical limit of massless gravitational scattering,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
N. Moynihan and J. Murugan, “On-Shell Electric-Magnetic Duality and the Dual Graviton,” arXiv:2002.11085 [hep-th]
Original
2002
Earlier work this paper cites.
E. Lescano and J. A. Rodríguez, “ 𝒩 \mathcal{N} = 1 supersymmetric Double Field Theory and the generalized Kerr-Schild ansatz,” JHEP
Original
2002
Earlier work this paper cites.
A. Cristofoli, P. H. Damgaard, P. Di Vecchia, and C. Heissenberg, “Second-order Post-Minkowskian scattering in arbitrary dimensions,” JHEP
Original
2003
Earlier work this paper cites.
B. R. Holstein and J. F. Donoghue, “Classical physics and quantum loops,” Phys. Rev. Lett
2004
Earlier work this paper cites.
A. Luna, S. Nagy, and C. D. White, “The convolutional double copy: a case study with a point,” arXiv:2004.11254 [hep-th]
Original
2004
Earlier work this paper cites.
L. Borsten and S. Nagy, “The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order,” JHEP
Original
2004
Earlier work this paper cites.
F. Pretorius, “Evolution of binary black hole spacetimes,” Phys. Rev. Lett
2005
Earlier work this paper cites.
Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, “Spinning black hole binary dynamics, scattering amplitudes, and effective field theory,” Phys. Rev. D
Original
2005
Earlier work this paper cites.
J. Parra-Martinez, M. S. Ruf, and M. Zeng, “Extremal black hole scattering at 𝒪 ⁡ ( G 3 ) \mathcal{O}(G^{3}) : graviton dominance, eikonal exponentiation, and differential equations,” JHEP
Original
2005
Earlier work this paper cites.
K. Haddad and A. Helset, “The double copy for heavy particles,” Phys. Rev. Lett
Original
2005
Earlier work this paper cites.
J. F. Donoghue, B. R. Holstein, B. Garbrecht, and T. Konstandin, “Quantum corrections to the Reissner-Nordström and Kerr-Newman metrics,” Phys. Lett. B
2005
Earlier work this paper cites.

Similar

N. E. J. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, “Quantum corrections to the Schwarzschild and Kerr metrics,” Phys. Rev. D
2005
Cited alongside, same era.
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
2005
Cited alongside, same era.
A. Falkowski and C. S. Machado, “Soft Matters, or the Recursions with Massive Spinors,” JHEP
Original
2005
Cited alongside, same era.
W. D. Goldberger and I. Z. Rothstein, “An Effective field theory of gravity for extended objects,” Phys. Rev. D
2006
Cited alongside, same era.
M. Accettulli Huber, A. Brandhuber, S. De Angelis, and G. Travaglini, “Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity,” Phys. Rev. D
Original

Then

A. Luna, R. Monteiro, I. Nicholson, D. O’Connell, and C. D. White, “The double copy: Bremsstrahlung and accelerating black holes,” JHEP
Original
2016
Later among the works it cites.
G. Cardoso, S. Nagy, and S. Nampuri, “A double copy for 𝒩 = 2 \mathcal{N}=2 supergravity: a linearised tale told on-shell,” JHEP
Original
2016
Later among the works it cites.
LIGO Scientific, Virgo
Original
2017
Later among the works it cites.
LIGO Scientific, Virgo
Original
2017
Later among the works it cites.
W. D. Goldberger and A. K. Ridgway, “Radiation and the classical double copy for color charges,” Phys. Rev. D
Original

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2022

NLO deflections for spinning particles and Kerr black holes

Menezes, Gabriel, Sergola, Matteo

Understand

We employ the "KMOC" formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop).

We do this in electrodynamics and gravity.
The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop.
Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order.

Built on

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
Original
1901
Earlier work this paper cites.
S. Foffa, R. A. Porto, I. Rothstein, and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian,” Phys. Rev. D
Original
1903
Earlier work this paper cites.
W. Cho and K. Lee, “Heterotic Kerr-Schild Double Field Theory and Classical Double Copy,” JHEP
Original
1904
Earlier work this paper cites.
W. T. Emond and N. Moynihan, “Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity,” JHEP
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, “Post-Minkowskian Hamiltonians in general relativity,” Phys. Rev. D
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell, and J. Vines, “Observables and amplitudes for spinning particles and black holes,” JHEP
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y.-t. Huang, and D. O’Connell, “Kerr black holes as elementary particles,” JHEP
Original
1906
Earlier work this paper cites.
H. Johansson and A. Ochirov, “Double copy for massive quantum particles with spin,” JHEP
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov, and J. Vines, “Black-hole scattering with general spin directions from minimal-coupling amplitudes,” Phys. Rev. D
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP
Original
1908
Earlier work this paper cites.
H. Godazgar, M. Godazgar, and C. Pope, “Taub-NUT from the Dirac monopole,” Phys. Lett. B
Original
1908
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The Duality Between Color and Kinematics and its Applications,” arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
N. Siemonsen and J. Vines, “Test black holes, scattering amplitudes and perturbations of Kerr spacetime,” Phys. Rev. D
Original
1909
Earlier work this paper cites.
N. Moynihan, “Kerr-Newman from Minimal Coupling,” JHEP
Original
1909
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” JHEP
Original
1910
Earlier work this paper cites.
I. Bah, R. Dempsey, and P. Weck, “Kerr-Schild Double Copy and Complex Worldlines,” JHEP
Original
1910
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist),” JHEP
Original
1911
Earlier work this paper cites.
R. Alawadhi, D. S. Berman, B. Spence, and D. Peinador Veiga, “S-duality and the double copy,” JHEP
Original
1911
Earlier work this paper cites.
Y.-T. Huang, U. Kol, and D. O’Connell, “Double copy of electric-magnetic duality,” Phys. Rev. D
Original
1911
Earlier work this paper cites.
W. D. Goldberger and J. Li, “Strings, extended objects, and the classical double copy,” JHEP
Original
1912
Earlier work this paper cites.
E. T. Newman and A. I. Janis, “Note on the Kerr spinning particle metric,” J. Math. Phys
1965
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B
1986
Earlier work this paper cites.
J. F. Donoghue, “Leading quantum correction to the Newtonian potential,” Phys. Rev. Lett
1994
Earlier work this paper cites.
J. F. Donoghue, “General relativity as an effective field theory: The leading quantum corrections,” Phys. Rev. D
1994
Earlier work this paper cites.
J. F. Donoghue and T. Torma, “On the power counting of loop diagrams in general relativity,” Phys. Rev. D
1996
Earlier work this paper cites.
Wiley, 1998
Original
J. D. Jackson, Classical Electrodynamics · 1998
Earlier work this paper cites.
A. Buonanno and T. Damour, “Effective one-body approach to general relativistic two-body dynamics,” Phys. Rev. D
1999
Earlier work this paper cites.
A. Buonanno and T. Damour, “Transition from inspiral to plunge in binary black hole coalescences,” Phys. Rev. D
2000
Earlier work this paper cites.
T. Damour, P. Jaranowski, and G. Schaefer, “On the determination of the last stable orbit for circular general relativistic binaries at the third postNewtonian approximation,” Phys. Rev. D
2000
Earlier work this paper cites.
T. Damour, “Coalescence of two spinning black holes: an effective one-body approach,” Phys. Rev. D
2001
Earlier work this paper cites.
Z. Bern, H. Ita, J. Parra-Martinez, and M. S. Ruf, “Universality in the classical limit of massless gravitational scattering,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
N. Moynihan and J. Murugan, “On-Shell Electric-Magnetic Duality and the Dual Graviton,” arXiv:2002.11085 [hep-th]
Original
2002
Earlier work this paper cites.
E. Lescano and J. A. Rodríguez, “ 𝒩 \mathcal{N} = 1 supersymmetric Double Field Theory and the generalized Kerr-Schild ansatz,” JHEP
Original
2002
Earlier work this paper cites.
A. Cristofoli, P. H. Damgaard, P. Di Vecchia, and C. Heissenberg, “Second-order Post-Minkowskian scattering in arbitrary dimensions,” JHEP
Original
2003
Earlier work this paper cites.
B. R. Holstein and J. F. Donoghue, “Classical physics and quantum loops,” Phys. Rev. Lett
2004
Earlier work this paper cites.
A. Luna, S. Nagy, and C. D. White, “The convolutional double copy: a case study with a point,” arXiv:2004.11254 [hep-th]
Original
2004
Earlier work this paper cites.
L. Borsten and S. Nagy, “The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order,” JHEP
Original
2004
Earlier work this paper cites.
F. Pretorius, “Evolution of binary black hole spacetimes,” Phys. Rev. Lett
2005
Earlier work this paper cites.
Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, “Spinning black hole binary dynamics, scattering amplitudes, and effective field theory,” Phys. Rev. D
Original
2005
Earlier work this paper cites.
J. Parra-Martinez, M. S. Ruf, and M. Zeng, “Extremal black hole scattering at 𝒪 ⁡ ( G 3 ) \mathcal{O}(G^{3}) : graviton dominance, eikonal exponentiation, and differential equations,” JHEP
Original
2005
Earlier work this paper cites.
K. Haddad and A. Helset, “The double copy for heavy particles,” Phys. Rev. Lett
Original
2005
Earlier work this paper cites.
J. F. Donoghue, B. R. Holstein, B. Garbrecht, and T. Konstandin, “Quantum corrections to the Reissner-Nordström and Kerr-Newman metrics,” Phys. Lett. B
2005
Earlier work this paper cites.

Similar

N. E. J. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, “Quantum corrections to the Schwarzschild and Kerr metrics,” Phys. Rev. D
2005
Cited alongside, same era.
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
2005
Cited alongside, same era.
A. Falkowski and C. S. Machado, “Soft Matters, or the Recursions with Massive Spinors,” JHEP
Original
2005
Cited alongside, same era.
W. D. Goldberger and I. Z. Rothstein, “An Effective field theory of gravity for extended objects,” Phys. Rev. D
2006
Cited alongside, same era.
M. Accettulli Huber, A. Brandhuber, S. De Angelis, and G. Travaglini, “Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity,” Phys. Rev. D
Original