From boundary data to bound states
By G. Kalin, Rafael A. Porto. Journal of High Energy Physics, 2019
235 citations recorded by the source corpus.
We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/b9cff4348c513120676d093ec3db1d3758d60c74
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Citations in the corpus
- Classical and quantum scattering in post-Minkowskian gravity (2019, background): “[Some of the results derived below (which have been presented in various talks [54]), have been recently discussed from quite different (nonEOB-based) perspectives in two papers [55, 56].”
- The amplitude for classical gravitational scattering at third Post-Minkowskian order (2021, background): “…Lippmann-Schwinger equation leads to explicit formulas for the scattering angle in terms of the coefficients of the relativistic two-body potential [11–13], in a sense thereby solving the problem of kinematics of the relativistic two-body problem in general relativity by means of quantum field…”
- Universality of ultra-relativistic gravitational scattering (2020, background): “There has been considerable interest, recently, in the use of new scattering amplitude techniques for extracting information about the conservative scattering process in the case s ∼ m(2)i [10, 11, 12, 13, 14, 15, 16, 17, 18]: the aim is to pin down the relevant ingredients needed for describing the”
- Radiative contribution to classical gravitational scattering at the third order in G (2020, methodology): “[18] G.”
- Classical black hole scattering from a worldline quantum field theory (2020, methodology): “etermine its conservative two-body potential [85,95]. The so-obtained eective potential is then used to compute observables such as the scattering angle or the periastron advance in the bound system [64,96,97]. Both approaches | involving the worldline EFT and modern scattering amplitudes | agree on”
- Post-Minkowskian effective field theory for conservative binary dynamics (2020, methodology): “owskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the de ection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1,2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both i”