Generic Spinning Binaries from the Scattering Amplitude Perspective
Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In conventional world-line formalism for spinning binaries in general relativity, one assumes that the dynamical degrees of freedom for spin are the completely captured by the rest frame canonical spin. A spin supplementary condition (SSC) is then necessary to remove redundancies. We study this problem from an amplitude-based field theory perspective. In higher spin field theories, it is notoriously difficult to impose transverse and traceless conditions when interactions are included. We take an alternative approach and keep the additional degrees of freedom. We see that for generic Wilson coefficients, we obtain a system with a dynamical mass dipole that has physical effect starting at the quadrupole level. It will decouple when we choose special values for Wilson coefficients, and we land back on the dynamics of conventional spinning binaries. The situation is very similar to a symmetry breaking in the classical limit. We also construct a world-line Lagrangian and a classical effective Hamiltonian that completely match the physics mentioned above, which incorporates a dynamical mass dipole as the additional dynamical degree of freedom. The mass dipole has physical effects, and its significance is a question for phenomenology. On the other hand, the dipole can be removed by an emergent world-line shift symmetry when Wilson coefficients take special values. From this perspective, our formalism can simplify the calculation for conventional spinning binaries, as the SSC constraint can be effectively relaxed.
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