Gravitational radiation from color-kinematics duality

157

182

The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

Section: Summary and Discussionmentioning

confidence: 97%

Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Double copy for massive quantum particles with spin

Johansson

Ochirov

2019

157

182

“…While only proven at tree-level for pure gauge theory [60], this conjecture can be applied to both massless and massive states [61,62] and has a wealth of non-trivial supporting evidence [63][64][65]. It raises the provocative question of whether exact solutions in general relativity satisfy similar simple relationships to their classical Yang-Mills counterparts, coined the classical double copy [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80]. Such a relationship has indeed been found in the gravitational radiation emitted by spinning sources at 1PM order [81,82].…”

Section: Introductionmentioning

confidence: 99%

Observables and amplitudes for spinning particles and black holes

Maybee¹,

O’Connell²,

Vines³

2019

252

272

We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.

“…8 Conclusion and Outlook 59 9 Acknowledgements 60 A Spinor-helicity variables 60 A.1 Lorentz algebra 60 A.2 Massless momenta 61 A.3 Massive momenta 62 A.4 High-Energy limit 63 A.5 Spin operator 66 A.6 Polarisation 67 B The normalization of Gravitomagnetic Zeeman coupling 68 C Some Details of the t-channel Matching of the Higher Spin Graviton Compton Amplitude 69 -ii -D Wilson coefficients for black holes 72 E Spin-orbit factor corrections to polarisation tensor contractions 73Recently there has been tremendous activity in applying advanced developments in perturbative QFT computations to the computation of such classical effects, commonly referred to as classical potentials. These include generalized unitarity methods [12,13], double copy relations [14][15][16][17], and spinor-helicity variables [2,3,[18][19][20][21]. Following Cachazo and Guevara [2, 3], we compute the spin-dependent pieces of the 2PM classical potential to cubic and quartic in either Black Hole's spin.…”

mentioning

confidence: 99%

The simplest massive S-matrix: from minimal coupling to black holes

Chung

Huang

Kim

et al. 2019

240

359

In this paper, we explore the physics of electromagnetically and gravitationally coupled massive higher spin states from the on-shell point of view. Starting with the threepoint amplitude, we focus on the simplest amplitude characterized by matching to minimal coupling in the UV. In the IR, for charged states this leads to g = 2 for arbitrary spin, and the leading deformation corresponds to the anomalous magnetic dipole moment. We proceed to construct the (gravitational) Compton amplitude for generic spins via consistent factorization. We find that in gravitation couplings, the leading deformation leads to inconsistent factorization. This implies that for systems with Gauge 2 = Gravity relations, such as perturbative string theory, all charged states must have g = 2. It is then natural to ask for generic spin, what is the theory that yields such minimal coupling. By matching to the one body effective action, we verify that for large spins the answer is Kerr black holes. This identification is then an on-shell avatar of the no-hair theorem. Finally using this identification as well as the newly constructed Compton amplitudes, we proceed to compute the spin-dependent pieces for the classical potential at 2PM order up to degree four in spin operator of either black holes. 8 Conclusion and Outlook 59 9 Acknowledgements 60 A Spinor-helicity variables 60 A.1 Lorentz algebra 60 A.2 Massless momenta 61 A.3 Massive momenta 62 A.4 High-Energy limit 63 A.5 Spin operator 66 A.6 Polarisation 67 B The normalization of Gravitomagnetic Zeeman coupling 68 C Some Details of the t-channel Matching of the Higher Spin Graviton Compton Amplitude 69 -ii -D Wilson coefficients for black holes 72 E Spin-orbit factor corrections to polarisation tensor contractions 73Recently there has been tremendous activity in applying advanced developments in perturbative QFT computations to the computation of such classical effects, commonly referred to as classical potentials. These include generalized unitarity methods [12,13], double copy relations [14][15][16][17], and spinor-helicity variables [2,3,[18][19][20][21]. Following Cachazo and Guevara [2, 3], we compute the spin-dependent pieces of the 2PM classical potential to cubic and quartic in either Black Hole's spin. Such corrections, to the best of authors' knowledge, have not been presented in the literature before.This paper is organized as follows. First, we start with a brief review of the massive spinor M ···{I 1 ,I 2 ,··· ,I 2s i }··· n(2.10)leaving behind a function that is symmetric in SL(2, C) indices instead. We will refer to this representation as the chiral basis, reflecting the fact that we are using the un-dotted SL(2, C) indices. One can equally use the anti-chiral basis, and the two can be converted to each other by contracting with p αα m . This separation will be useful when considering suitable basis for all possible three-point interactions as we will now see. General structure of the three-point amplitudeWe now consider the most general form of the three-point amplitude fo...