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Renormalizing Love: tidal effects at the third post-Newtonian order

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 23 February 2024
  • Volume 2024, article number 188, (2024)
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Journal of High Energy Physics Aims and scope Submit manuscript
Renormalizing Love: tidal effects at the third post-Newtonian order
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  • Manoj K. Mandal  ORCID: orcid.org/0000-0003-0850-76851,2,3,
  • Pierpaolo Mastrolia  ORCID: orcid.org/0000-0001-9711-77981,2,
  • Hector O. Silva  ORCID: orcid.org/0000-0002-0066-94714,
  • Raj Patil  ORCID: orcid.org/0000-0002-7055-03454,5 &
  • …
  • Jan Steinhoff  ORCID: orcid.org/0000-0002-1614-02144 

  • 342 Accesses

  • 7 Citations

  • 1 Altmetric

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A preprint version of the article is available at arXiv.

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.

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Acknowledgments

We thank Sumanta Chakraborty, Thibault Damour, Rossella Gamba, Quentin Henry, Mikhail Ivanov, Gustav Jakobsen, Jung-Wook Kim, Oliver Long, Elisa Maggio, Saketh MVS, Alessandro Nagar, Ira Rothstein and Justin Vines for insightful comments and discussions. We would like to thank authors of [137] for pointing out a typo in equation (6.14). 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 No. 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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Authors and Affiliations

  1. Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Marzolo 8, I-35131, Padova, Italy

    Manoj K. Mandal & Pierpaolo Mastrolia

  2. INFN, Sezione di Padova, Via Marzolo 8, I-35131, Padova, Italy

    Manoj K. Mandal & Pierpaolo Mastrolia

  3. Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, CA, 90095, USA

    Manoj K. Mandal

  4. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476, Potsdam, Germany

    Hector O. Silva, Raj Patil & Jan Steinhoff

  5. Institut für Physik und IRIS Adlershof, Humboldt-Universit ät zu Berlin, Zum Großen Windkanal 2, D-12489, Berlin, Germany

    Raj Patil

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Mandal, M.K., Mastrolia, P., Silva, H.O. et al. Renormalizing Love: tidal effects at the third post-Newtonian order. J. High Energ. Phys. 2024, 188 (2024). https://doi.org/10.1007/JHEP02(2024)188

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  • Received: 08 September 2023

  • Revised: 19 January 2024

  • Accepted: 12 February 2024

  • Published: 23 February 2024

  • DOI: https://doi.org/10.1007/JHEP02(2024)188

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Keywords

  • Black Holes
  • Effective Field Theories
  • Renormalization and Regularization
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