Abstract
We present a gravitoelectric quadrupolar dynamical tidal-interaction Hamiltonian for a compact binary system, that is valid to second order in the post-Newtonian expansion. Our derivation uses the diagrammatic effective field theory approach, and involves Feynman integrals up to two loops, evaluated with the dimensional regularization scheme. We also derive the effective Hamiltonian for adiabatic tides, obtained by taking the appropriate limit of the dynamical effective Hamiltonian, and we check its validity by verifying the complete Poincaré algebra. In the adiabatic limit, we also calculate two gauge-invariant observables, namely, the binding energy for a circular orbit and the scattering angle in a hyperbolic scattering. Our results are important for developing accurate gravitational waveform models for neutron-star binaries for present and future gravitational-wave observatories.
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Acknowledgments
We thank Quentin Henry, Gustav Jakobsen, Jung-Wook Kim, Saketh MVS, and Sebastian Völkel for insightful discussions. We are particularly grateful to Quentin Henry who provided us the Hamiltonian obtained in ref. [36], which we used to validate some of our results. We thank Marcus Haberland for pointing out a typo in equation (5.15). The figures in this work were produced with TikZ [101]. The work of M.K.M is supported by Fellini - Fellowship for Innovation at INFN funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754496. H.O.S acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) - project number: 386119226. R.P.’s research is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory”.
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Mandal, M.K., Mastrolia, P., Silva, H.O. et al. Gravitoelectric dynamical tides at second post-Newtonian order. J. High Energ. Phys. 2023, 67 (2023). https://doi.org/10.1007/JHEP11(2023)067
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DOI: https://doi.org/10.1007/JHEP11(2023)067