Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order

Bern, Zvi; Cheung, Clifford; Roiban, Radu; Shen, Chia Hsien; Solon, Mikhail P.; Zeng, M.

doi:10.1103/physrevlett.122.201603

Cited by 516 publications

(641 citation statements)

References 91 publications

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“…It would be interesting to understand whether the discrepancy mentioned above is related to the different kinematics where the two exponentiations are valid 17 . Clarifying this point may be relevant beyond the N = 8 case studied in this work, since now, even for the physically interesting case of the massive scattering in CGR, the focus is on 3PM and higher order corrections [45,46] where such subtleties may play some role. (STFC) Consolidated Grant ST/P000754/1 "String theory, gauge theory and duality, and/or by the European Union Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No.…”

Section: Discussionmentioning

confidence: 88%

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A tale of two exponentiations in N=8 supergravity

et al. 2019

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High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent threeloop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ǫ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

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Section: Discussionmentioning

confidence: 88%

“…An exception is 't Hooft's 1987 calculation[10] which is carried out assuming a non-trivial background metric 2. Recently, impressive amplitude calculations have also been carried out for the collision of massive (and typically non-relativistic) particles up the two-loop (3PM) order[45,46] and their outcome was incorporated into the EOB potential[47].…”

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confidence: 99%

A tale of two exponentiations in N=8 supergravity

et al. 2019

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“…The derivatives with respect to J and E gave us the periastron advance and radial frequency, while the remaining one yields Using the general formulas in (4.9) and (4.10) we can now construct all dynamical invariants using the state-of-the-art knowledge of the scattering angle to two-loops. The relevant scattering amplitude was computed in [17,18], leading to the PM coefficients…”

Section: Redshiftmentioning

confidence: 99%

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

Kälin

Porto

2020

J. High Energ. Phys.

202

261

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We recently introduced in [1910.03008] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following -remarkably simple -formula relating the periastron advance to the scattering angle: ∆Φ(J, E) = χ(J, E) + χ(−J, E), via analytic continuation in angular momentum and binding energy. Using explicit expressions from [1910.03008], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude.As an example, we reproduce our result in [1910.03008] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test-and two-body dynamics, we also compute the periastron advance up to quadratic order in the spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized 'impetus formula' for spinning bodies and black holes as 'elementary particles'. Our findings here and in [1910.03008] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.

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“…The value of the 2PM, O(G 2 ), term u 2 Q ν2 (H S ) has been computed in Ref. [10], while the value of the 3PM, O(G 3 ), term u 3 Q ν3 (H S ) is still a matter of debate [15,21,22,63]. The additional, tidal-related contribution Q tidal in Eq.…”

Section: Transcription Of the Tidal Actions Within The Eob Formalismmentioning

confidence: 99%

“…where the term of order α 2 is negligible because h ≈ √ 2νγ → ∞. There is a current debate about the recently computed 3PM O(G 3 ) contribution [21,22] which yields a divergent G 3 contribution, O(α 3 ln(γ) → ∞ as γ → ∞, while the computation of Ref. [66] (see also [30]) got a finite O(α 3 ) correction in the massless limit.…”

Section: Tidal Contribution To the Scattering Angle And To Periasmentioning

confidence: 99%

Scattering of tidally interacting bodies in post-Minkowskian gravity

2020

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The post-Minkowskian approach to gravitationally interacting binary systems (i.e., perturbation theory in G, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the first post-Minkowskian order. The corresponding contributions to the scattering angle are derived.

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Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order

Cited by 516 publications

References 91 publications

A tale of two exponentiations in N=8 supergravity

A tale of two exponentiations in N=8 supergravity

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

Scattering of tidally interacting bodies in post-Minkowskian gravity

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