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

Abstract

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...

Double copy of massive scalar QCD

“…with L adg the two-form-dilaton-gravity theory of (28). Note that in 4D upon dualizing the two-form to an axion 2 We thank Alexander Ochirov for crucial discussions on this point.…”

Kerr-Newman from minimal coupling

“…At tree level, there is only one possible diagram that we can consider Since there is no electromagnetic interaction, this will simply produce a purely gravitational interaction at order G, and has been calculated many times in the literature [1,27,28].…”

“…While the original aim of the double copy program was to simplify loop computations in gravity, it has found many uses in classical gravity, from metric reconstruction [13][14][15][16][17][18][19][20] to gravitational wave physics [21][22][23][24]. In particular, the introduction of a formalism to compute amplitudes of arbitrary mass and spin [25] has provided a powerful way to investigate spin effects in classical observables [24,[26][27][28][29]. Calculations involving spin effects in gravity are often computed in the post-Newtonian (small velocities v ≪ c) or post-Minkowskian (expansion in G) frameworks [30][31][32][33][34][35][36][37][38], however there have also been calculations involving loop amplitudes via standard Feynman diagram techniques and form factors [39,40].…”

“…Furthermore, we show explicitly that the relevant amplitudes themselves factorise into a spin-independent piece and a spin factor, as was demonstrated in the case of Kerr black holes in Refs. [1,27,51]. Very recently, it was shown that this factorization, in the infinite spin limit, is the on-shell avatar of the Janis-Newman algorithm [1], which utilises a complex coordinate transformation of the Schwarzchild (Riessner-Nordström) solution leading directly to the Kerr (Kerr-Newman) solution [52,53].…”

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

“…Even though, at this stage we resort to the existence of the quasi-isotropic gauge, this is ultimately the one (implicitly) chosen by the Fourier transform of the amplitude in the center of mass frame. Therefore, provided the matching discussed in [15][16][17][18] carries over to spin, as suggested in [19][20][21][22][23][24][25][26], the existence of this gauge is guarantee to all PM orders. As before, the exact form of the Hamiltonian is never needed, although it may be obtained and shown to agree with the existent literature, e.g.…”