We compute the classical tree-level five-point amplitude for the two-to-two scattering of spinning celestial objects with the emission of a graviton. Using this five-point amplitude, we then turn to the computation of the leading-order time-domain gravitational waveform. The method we describe is suitable for arbitrary values of classical spin of Kerr black holes and does not require any expansion in powers of the spin. In this paper we illustrate it in the simpler case of the scattering of one Kerr and one Schwarzschild black hole. An important ingredient of our calculation is a novel form of the Compton amplitude with spinning particles including contact terms derived from matching to black-hole perturbation theory calculations. This ensures that our waveform is valid up to at least fourth order in the spin. Our method can be applied immediately to generate improved waveforms once higher-order contact terms in the Compton amplitude become available. Finally, we show the formula for the gravitational memory to all orders in the spin, which is in agreement with our results.

United Kingdom

Andreas Brandhuber

Graham Brown

Denmark

Gang Chen

Joshua Gowdy

Gabriele Travaglini

Resummed spinning waveforms from five-point amplitudes

We explore the double copy for self-dual gauge and gravitational fields on self-dual background spacetimes. We consider backgrounds associated with solutions of the second Plebanski equation and describe results with different gauge-fixing conditions. Finally we discuss the kinematic and <math><mi>w</mi></math>-algebras and the double copy, identifying modified Poisson structures and kinematic structure constants in the presence of the self-dual background. The self-dual plane wave and Eguchi-Hanson spacetimes are studied as examples and their respective <math><mi>w</mi></math>-algebras derived.

Graham R. Brown

Bill Spence

Self-dual fields on self-dual backgrounds and the double copy

We show how to formulate celestial twistor amplitudes in Yang-Mills (YM) and gravity. This is motivated by a refined holographic correspondence between the twistor transform and the light transform in the boundary Lorentzian CFT. The resulting amplitudes are then equivalent to light transformed correlators on the celestial torus. Using an ambidextrous basis of twistor and dual twistor variables, we derive formulas for the three- and four-point YM and gravity amplitudes. The four-point amplitudes take a particularly simple form in terms of elementary functions, with a striking correspondence between the YM and gravity expressions. We derive celestial twistor Britto–Cachazo–Feng–Witten recursion relations and show how these may be used to generate the four-point YM amplitude, illuminating the structure it inherits from the three-point amplitude and paving the way for the calculation of higher multiplicity light transformed correlators. Throughout our calculations we utilize the unique properties of the boundary structure of split signature, and in order to properly motivate and highlight these properties, we first develop our methodology in Lorentzian signature. This also allows us to prove a holographic correspondence between Fourier transforms in Lorentzian signature and shadow transforms in the Euclidean boundary CFT.

United States

Celestial twistor amplitudes

Using a heavy-mass effective field theory (HEFT), we study gravitational-wave emission in the scattering of two spinless black holes or neutron stars of arbitrary masses at next-to-leading order in the Post-Minkowskian expansion. We compute the contributions to the one-loop scattering amplitude with four scalars and one graviton which are relevant to the calculation of the waveforms, also presenting expressions of classical tree-level amplitudes with four scalars and up to two radiated gravitons. The latter are obtained using a novel on-shell recursion relation for classical amplitudes with four scalars and an arbitrary number of gravitons. Our one-loop five-point amplitude is expressed in terms of a single family of master integrals with the principal value prescription for linearised massive propagators, which we evaluate using differential equations. In our HEFT approach, soft/heavy-mass expansions of complete integrands are avoided, and all hyper-classical iterations and quantum corrections are dropped at the diagrammatic level, thereby computing directly contributions to classical physics. Our result exhibits the expected factorisation of infrared divergences, the correct soft limits, and highly nontrivial cancellations of spurious poles. Finally, using our amplitude result we compute numerically the corresponding next-to-leading corrections to the spectral waveforms and the far-field time-domain waveforms using the Newman-Penrose scalar Ψ4.

France

Stefano Angelis

One-loop gravitational bremsstrahlung and waveforms from a heavy-mass effective field theory

It was recently proposed that the kinematic algebra featuring in the colour-kinematics duality for scattering amplitudes in heavy-mass effective field theory (HEFT) and Yang-Mills theory is a quasi-shuffle Hopf algebra. The associated fusion product determines the structure of the Bern-Carrasco-Johansson (BCJ) numerators, which are manifestly gauge invariant and with poles corresponding to heavy-particle exchange. In this work we explore the deep connections between the quasi-shuffle algebra and general physical properties of the scattering amplitudes. First, after proving the double-copy form for gravitational HEFT amplitudes, we show that the coproducts of the kinematic algebra are in correspondence with factorisations of BCJ numerators on massive poles. We then study an extension of the standard quasi-shuffle Hopf algebra to a non-abelian version describing BCJ numerators with all possible gluon orderings. This is achieved by tensoring the original algebra with a particular Hopf algebra of orderings. In this extended version, a specific choice of the coproduct in the algebra of orderings leads to an antipode in the resulting Hopf algebra that has the interpretation of reversing the gluons’ order within each BCJ numerator.

Congkao Wen

Amplitudes, Hopf algebras and the colour-kinematics duality

We study celestial amplitudes in (super) Yang-Mills theory using a parametrization of the spinor helicity variables where their overall phase is not fixed by the little group action. In this approach the spin constraint <math><mi>h</mi><mo>−</mo><mover><mi>h</mi><mo>¯</mo></mover><mo>=</mo><mi>J</mi></math> for celestial conformal primaries emerges naturally from a new Mellin transform, and the action of conformal transformations on celestial amplitudes is derived. Applying this approach to <math><mi>N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills, we show how the appropriate definition of on-shell superspace coordinates leads naturally to a formulation of chiral celestial superamplitudes and a representation of the generators of the four-dimensional superconformal algebra on the celestial sphere, which by construction annihilate all tree-level celestial superamplitudes.