Classical gravitational scattering at $$ \mathcal{O} $$(G3) from Feynman diagrams

Cheung, Clifford; Solon, Mikhail P.

doi:10.1007/jhep06(2020)144

Cited by 132 publications

(77 citation statements)

References 98 publications

(156 reference statements)

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“…[19,20] in the case of Einstein gravity. Since then, the correctness of the latter result has been verified at high orders in the velocity expansion [48,49], an alternative method for resummation of the velocity series has been used with identical results [50], and the unitarity cut construction of the loop integrand has been checked against direct Feynman diagram computations [51]. Still, a direct relativistic calculation that bypasses velocity resummation will be a valuable additional confirmation of the result, and will provide a way to streamline future calculations at O(G 3 ) and beyond.…”

Section: Jhep11(2020)023mentioning

confidence: 99%

Extremal black hole scattering at $$ \mathcal{O} $$(G3): graviton dominance, eikonal exponentiation, and differential equations

Parra-Martinez¹,

Ruf

Zeng

2020

J. High Energ. Phys.

149

211

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We use $$ \mathcal{N} $$ N = 8 supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at $$ \mathcal{O} $$ O (G3) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known D-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.

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Section: Jhep11(2020)023mentioning

confidence: 99%

Extremal black hole scattering at $$ \mathcal{O} $$(G3): graviton dominance, eikonal exponentiation, and differential equations

Parra-Martinez¹,

Ruf

Zeng

2020

J. High Energ. Phys.

149

211

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“…Transforming to impact parameter space b by means of a Fourier transform in D − 2 dimensions yields 20) while the same Fourier transform for the tree level amplitude (3.7) gives…”

Section: Eikonal Exponentiation and Unitaritymentioning

confidence: 99%

“…Given the expected improvements in detector sensitivity, it will be extremely important in the future to have high-precision theoretical predictions from General Relativity. To this aim the use of quantum field theory amplitudes to extract the post-Minkowskian (PM) expansion of General Relativity has recently gained considerable momentum [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and progress is now also being made on extensions to spinning objects [22][23][24][25][26][27][28][29][30][31]. The underlying physical motivation for this approach lies in the observation that, during the early stages of a merger event, when the two compact objects are still far apart, gravitational interactions are weak and can be conveniently treated JHEP07(2020)122 in a weak-coupling approximation.…”

Section: Introductionmentioning

confidence: 99%

Second-order post-Minkowskian scattering in arbitrary dimensions

Cristofoli

Damgaard

Vecchia

et al. 2020

J. High Energ. Phys.

126

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We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

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“…Comprehensive reviews on this topic from different perspective can be found in [37][38][39][40]. In the post-Minkowskian framework, which is natural in the context of amplitudes, the current state of the art is at 3PM order [41,42], a result which was recently confirmed in [35,43]. Note also the effective one-body approach of [44], recently extended to incorporate the first and second post-Minkowskian corrections in [45,46], respectively.…”

Section: A Overviewmentioning

confidence: 97%

Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity

et al. 2020

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The eikonal approximation is an ideal tool to extract classical observables in gauge theory and gravity directly from scattering amplitudes. Here we consider effective theories of gravity where in addition to the Einstein-Hilbert term we include nonminimal couplings of the type R 3 , R 4 and FFR. In particular, we study the scattering of gravitons and photons of frequency ω off heavy scalars of mass m in the limit m ≫ ω ≫ j⃗ qj, where ⃗ q is the momentum transfer. The presence of nonminimal couplings induces helicityflip processes which survive the eikonal limit, thereby promoting the eikonal phase to an eikonal phase matrix. We obtain the latter from the relevant two-to-two helicity amplitudes that we compute up to oneloop order, and confirm that the leading-order terms in ω exponentiateà la Amati, Ciafaloni and Veneziano. From the eigenvalues of the eikonal phase matrix we then extract two physical observables, to 2PM order: the classical deflection angle and Shapiro time delay/advance. Whenever the classical expectation of helicity conservation of the massless scattered particle is violated, i.e., the eigenvalues of the eikonal matrix are nondegenerate, causality violation due to time advance is a generic possibility for small impact parameter. We show that for graviton scattering in the R 4 and FFR theories, time advance is circumvented if the couplings of these interactions satisfy certain positivity conditions, while it is unavoidable for graviton scattering in the R 3 theory and photon scattering in the FFR theory. The scattering processes we consider mimic the deflection of photons and gravitons off spinless heavy objects such as black holes.

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Classical gravitational scattering at $$ \mathcal{O} $$(G3) from Feynman diagrams

Cited by 132 publications

References 98 publications

Extremal black hole scattering at $$ \mathcal{O} $$(G3): graviton dominance, eikonal exponentiation, and differential equations

Extremal black hole scattering at $$ \mathcal{O} $$(G3): graviton dominance, eikonal exponentiation, and differential equations

Second-order post-Minkowskian scattering in arbitrary dimensions

Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity

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