| 1. |
- Collado, Arnau Koemans, et al.
(author)
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Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes
- 2019
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In: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 100:6
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Journal article (peer-reviewed)abstract
- In this paper we study the two-body gravitational scattering of massive scalars with different masses in general spacetime dimensions. We focus on the Regge limit (eikonal regime) of the resulting scattering amplitudes and discuss how to extract the classical information representing the scattering of two black holes. We derive the leading eikonal and explicitly show the resummation of the first leading energy contribution up to second order in Newton's gravitational constant. We also calculate the subleading eikonal showing that in general spacetime dimensions it receives a nontrivial contribution from the box integral. From the eikonal we extract the two-body classical scattering angle between the two black holes up to the second post-Minkowskian order. Taking various probe-limits of the two-body scattering angles we are able to show agreement between our results and various results in the literature. We highlight that the box integral also has a log-divergent (in energy) contribution at subsubleading order which violates perturbative unitarity in the ultrarelativistic limit. We expect this term to play a role in the calculation of the eikonal at the third post-Minkowskian order.
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| 2. |
- D'Appollonio, Giuseppe, et al.
(author)
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A microscopic description of absorption in high-energy string-brane collisions
- 2016
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In: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :3
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Journal article (peer-reviewed)abstract
- We study the collision of a highly energetic light closed string off a stack of Dp-branes at (sub)string-scale impact parameters and in a regime justifying a perturbative treatment. Unlike at larger impact parameters - where elastic scattering and/or tidal excitations dominate - here absorption of the closed string by the brane system, with the associated excitation of open strings living on it, becomes important. As a first step, we study this phenomenon at the disk level, in which the energetic closed string turns into a single heavy open string at rest whose particularly simple properties are described.
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| 3. |
- D'Appollonio, Giuseppe, et al.
(author)
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Microscopic unitary description of tidal excitations in high-energy string-brane collisions
- 2013
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In: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :11, s. 126-
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Journal article (peer-reviewed)abstract
- The eikonal operator was originally introduced to describe the effect A tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high-energy behaviour of the covariant string amplitudes, showing how to take into account the energy factors that enhance the contribution of the longitudinally polarized massive states in a simple way.
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| 4. |
- Di Vecchia, Paolo, et al.
(author)
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A tale of two exponentiations in N=8 supergravity at subleading level
- 2020
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In: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :3
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Journal article (peer-reviewed)abstract
- 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 three-loop 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 epsilon, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.
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| 5. |
- Di Vecchia, Paolo, et al.
(author)
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Angular momentum of zero-frequency gravitons
- 2022
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In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :8
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Journal article (peer-reviewed)abstract
- By following closely Weinberg's soft theorem, which captures the 1/omega pole contribution to the amplitude for soft graviton emissions (omega < Lambda on top of an arbitrary background hard process, we calculate the expectation value of the graviton's angular momentum operator for arbitrary collisions dressed with soft radiation. We find that the result becomes independent of the cutoff Lambda on the graviton's frequency, effectively localizing at omega = 0. In this way, our result captures the contribution to the angular momentum that comes from the zero-frequency modes. Like the soft theorem, our formula has an exact dependence on the kinematics of the hard particles and is only a function of their momenta. As an example, we discuss in some detail the case of the 2 -> 2 scattering of spinless particles in General Relativity and N = 8 supergravity.
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| 6. |
- Di Vecchia, Paolo, et al.
(author)
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Classical gravitational observables from the Eikonal operator
- 2023
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In: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 843
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Journal article (peer-reviewed)abstract
- We propose two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons and show how to compute from them different classical observables. In the first proposal, only genuinely propagating gravitons are included, while, in the second, zero-frequency modes are added in order to recover the effects of a static gravitational field. We first calculate the radiated energy momentum and the change in each particle's momentum, or impulse, to 3PM order finding agreement with the literature. We then calculate the angular momentum of the gravitational field after the collision. In order to do so, we adapt the method of reverse unitarity to the presence of derivatives in the operators describing the angular momentum and reproduce the result of [1] obtained by resumming the small-velocity expansion. As a new application, we derive also the variation in each particle's angular momentum up to 3PM: calculating separately field and particle contributions allows us to check the balance laws explicitly. We also show how the eikonal operator encodes the linear-response formula of Bini-Damour by deriving the linear radiation-reaction contribution to the transverse impulse at 4PM.
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| 7. |
- Di Vecchia, Paolo, et al.
(author)
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Radiation reaction from soft theorems
- 2021
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In: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 818
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Journal article (peer-reviewed)abstract
- Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.
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| 8. |
- Di Vecchia, Paolo, et al.
(author)
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The eikonal approach to gravitational scattering and radiation at O(G(3))
- 2021
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In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :7
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Journal article (peer-reviewed)abstract
- Using N = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat N = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein's gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.
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| 9. |
- Di Vecchia, Paolo, et al.
(author)
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The eikonal operator at arbitrary velocities I : The soft-radiation limit
- 2022
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In: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :7
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Journal article (peer-reviewed)abstract
- Observables related to the real part of the gravitational eikonal, such as the deflection angle and time delay, have been found so far to have a smooth post-Minkowskian (PM) expansion whose validity extends from the non-relativistic to the most extreme ultra-relativistic (UR) regime, which smoothly connects with massless particle collisions. To describe gravitational radiation, the eikonal phase has to be promoted to a unitary operator for which we motivate a proposal and start discussing properties in the soft-radiation limit. A convergent PM expansion is found to only hold below an UR bound (discussed in the GR literature in the seventies) above which a different expansion is instead needed implying, in general, some non-analyticity in Newton's constant. In this extreme UR regime soft radiative observables receive contributions only from gravitons and are therefore universal. This generalises the pattern discussed in [1] beyond the elastic case.
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| 10. |
- Di Vecchia, Paolo, et al.
(author)
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Universality of ultra-relativistic gravitational scattering
- 2020
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In: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 811
-
Journal article (peer-reviewed)abstract
- We discuss the ultra-relativistic gravitational scattering of two massive particles at two-loop (3PM) level. We find that in this limit the real part of the eikonal, determining the deflection angle, is universal for gravitational theories in the two derivative approximation. This means that, regardless of the number of supersymmetries or the nature of the probes, the result connects smoothly with the massless case discussed since the late eighties by Amati, Ciafaloni and Veneziano. We analyse the problem both by using the analyticity and crossing properties of the scattering amplitudes and, in the case of the maximally supersymmetric theory, by explicit evaluation of the 4-point 2-loop amplitude using the results for the integrals in the full soft region. The first approach shows that the observable we are interested in is determined by the inelastic tree-level amplitude describing the emission of a graviton in the high-energy double-Regge limit, which is the origin of the universality property mentioned above. The second approach strongly suggests that the inclusion of the whole soft region is a necessary (and possibly sufficient) ingredient for recovering ultra relativistic finiteness and universality at the 3PM level. We conjecture that this universality persists at all orders in the PM expansion.
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