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High Energy Physics - Theory, hep-th, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We present the conservative effective two-body Hamiltonian at the third order
in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical
tidal-interactions. Our derivation of the effective two-body Lagrangian is
based on the diagrammatic effective field theory approach and it involves
Feynman integrals up to three loops, which are evaluated within the dimensional
regularization scheme. The elimination of the divergent terms occurring in the
effective Lagrangian requires the addition of counterterms to ensure finite
observables, thereby introducing a renormalization group flow to the
post-adiabatic Love number. As a limiting case of the renormalized dynamical
effective Hamiltonian, we also derive the effective Hamiltonian for adiabatic
tides, and, in this regime, calculate the binding energy for a circular orbit,
and the scattering angle in a hyperbolic scattering.
