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Efficient resummation of high post-Newtonian contributions to the binding energy

Journal of High Energy Physics volume 2021, Article number: 165 (2021) Cite this article

A preprint version of the article is available at arXiv.

Abstract

A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more “efficient” observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods.

References

  1. T. Damour, P. Jaranowski and G. Schäfer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89 (2014) 064058 [arXiv:1401.4548] [INSPIRE].

  2. T. Damour, P. Jaranowski and G. Schäfer, Fourth post-Newtonian effective one-body dynamics, Phys. Rev. D 91 (2015) 084024 [arXiv:1502.07245] [INSPIRE].

  3. T. Damour, P. Jaranowski and G. Schäfer, Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity, Phys. Rev. D 93 (2016) 084014 [arXiv:1601.01283] [INSPIRE].

  4. L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation, Phys. Rev. D 93 (2016) 084037 [arXiv:1512.02876] [INSPIRE].

  5. L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order, Phys. Rev. D 95 (2017) 044026 [arXiv:1610.07934] [INSPIRE].

  6. L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order, Phys. Rev. D 96 (2017) 104043 [arXiv:1706.08480] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  7. T. Marchand, L. Bernard, L. Blanchet and G. Faye, Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order, Phys. Rev. D 97 (2018) 044023 [arXiv:1707.09289] [INSPIRE].

  8. L. Bernard, L. Blanchet, G. Faye and T. Marchand, Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order, Phys. Rev. D 97 (2018) 044037 [arXiv:1711.00283] [INSPIRE].

  9. S. Foffa and R. Sturani, Dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant, Phys. Rev. D 87 (2013) 064011 [arXiv:1206.7087] [INSPIRE].

  10. S. Foffa, P. Mastrolia, R. Sturani and C. Sturm, Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant, Phys. Rev. D 95 (2017) 104009 [arXiv:1612.00482] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. S. Foffa and R. Sturani, Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian, Phys. Rev. D 100 (2019) 024047 [arXiv:1903.05113] [INSPIRE].

  12. S. Foffa, R.A. Porto, I. Rothstein and R. Sturani, Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian, Phys. Rev. D 100 (2019) 024048 [arXiv:1903.05118] [INSPIRE].

  13. J. Blümlein, A. Maier, P. Marquard and G. Schäfer, Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach, Nucl. Phys. B 955 (2020) 115041 [arXiv:2003.01692] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  14. L. Lindblom, B.J. Owen and D.A. Brown, Model Waveform Accuracy Standards for Gravitational Wave Data Analysis, Phys. Rev. D 78 (2008) 124020 [arXiv:0809.3844] [INSPIRE].

    ADS  Article  Google Scholar 

  15. A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, Energetics of two-body Hamiltonians in post-Minkowskian gravity, Phys. Rev. D 99 (2019) 104004 [arXiv:1901.07102] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  16. LIGO Scientific collaboration, Advanced LIGO, Class. Quant. Grav. 32 (2015) 074001 [arXiv:1411.4547] [INSPIRE].

  17. VIRGO collaboration, Advanced Virgo: a second-generation interferometric gravitational wave detector, Class. Quant. Grav. 32 (2015) 024001 [arXiv:1408.3978] [INSPIRE].

  18. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Class. Quant. Grav. 27 (2010) 194002 [INSPIRE].

    ADS  Article  Google Scholar 

  19. LISA collaboration, Laser Interferometer Space Antenna, arXiv:1702.00786 [INSPIRE].

  20. T. Ledvinka, G. Schaefer and J. Bicak, Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation, Phys. Rev. Lett. 100 (2008) 251101 [arXiv:0807.0214] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. L. Blanchet and A.S. Fokas, Equations of motion of self-gravitating N -body systems in the first post-Minkowskian approximation, Phys. Rev. D 98 (2018) 084005 [arXiv:1806.08347] [INSPIRE].

  22. S. Foffa, Gravitating binaries at 5PN in the post-Minkowskian approximation, Phys. Rev. D 89 (2014) 024019 [arXiv:1309.3956] [INSPIRE].

  23. T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE].

  24. C. Cheung, I.Z. Rothstein and M.P. Solon, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett. 121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].

    ADS  Article  Google Scholar 

  25. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].

    ADS  Article  Google Scholar 

  26. T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102 (2020) 024060 [arXiv:1912.02139] [INSPIRE].

  27. Z. Bern, H. Ita, J. Parra-Martinez and M.S. Ruf, Universality in the classical limit of massless gravitational scattering, Phys. Rev. Lett. 125 (2020) 031601 [arXiv:2002.02459] [INSPIRE].

  28. P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Universality of ultra-relativistic gravitational scattering, Phys. Lett. B 811 (2020) 135924 [arXiv:2008.12743] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  29. T. Damour, Radiative contribution to classical gravitational scattering at the third order in G, Phys. Rev. D 102 (2020) 124008 [arXiv:2010.01641] [INSPIRE].

    ADS  Article  Google Scholar 

  30. W.D. Goldberger and I.Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  31. S. Foffa, P. Mastrolia, R. Sturani, C. Sturm and W.J. Torres Bobadilla, Static two-body potential at fifth post-Newtonian order, Phys. Rev. Lett. 122 (2019) 241605 [arXiv:1902.10571] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  32. J. Blümlein, A. Maier and P. Marquard, Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses, Phys. Lett. B 800 (2020) 135100 [arXiv:1902.11180] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  33. J. Blümlein, A. Maier, P. Marquard and G. Schäfer, Testing binary dynamics in gravity at the sixth post-Newtonian level, Phys. Lett. B 807 (2020) 135496 [arXiv:2003.07145] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  34. S. Foffa and R. Sturani, Hereditary terms at next-to-leading order in two-body gravitational dynamics, Phys. Rev. D 101 (2020) 064033 [arXiv:1907.02869] [INSPIRE].

  35. S. Foffa and R. Sturani, Tail terms in gravitational radiation reaction via effective field theory, Phys. Rev. D 87 (2013) 044056 [arXiv:1111.5488] [INSPIRE].

  36. R.A. Porto and I.Z. Rothstein, Apparent ambiguities in the post-Newtonian expansion for binary systems, Phys. Rev. D 96 (2017) 024062 [arXiv:1703.06433] [INSPIRE].

  37. D. Bini, T. Damour and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123 (2019) 231104 [arXiv:1909.02375] [INSPIRE].

    ADS  Article  Google Scholar 

  38. D. Bini, T. Damour and A. Geralico, Sixth post-Newtonian local-in-time dynamics of binary systems, Phys. Rev. D 102 (2020) 024061 [arXiv:2004.05407] [INSPIRE].

  39. D. Bini, T. Damour and A. Geralico, Sixth post-Newtonian nonlocal-in-time dynamics of binary systems, Phys. Rev. D 102 (2020) 084047 [arXiv:2007.11239] [INSPIRE].

  40. D. Bini, T. Damour, A. Geralico, S. Laporta and P. Mastrolia, Gravitational dynamics at O(G6 ): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [INSPIRE].

  41. G. Kälin and R.A. Porto, From Boundary Data to Bound States, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  42. G. Kälin and R.A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].

  43. G. Kälin, Z. Liu and R.A. Porto, Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach, Phys. Rev. Lett. 125 (2020) 261103 [arXiv:2007.04977] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  44. J. Vines, J. Steinhoff and A. Buonanno, Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order, Phys. Rev. D 99 (2019) 064054 [arXiv:1812.00956] [INSPIRE].

  45. S. Foffa and R. Sturani, Effective field theory calculation of conservative binary dynamics at third post-Newtonian order, Phys. Rev. D 84 (2011) 044031 [arXiv:1104.1122] [INSPIRE].

  46. S. Foffa and R. Sturani, Effective field theory methods to model compact binaries, Class. Quant. Grav. 31 (2014) 043001 [arXiv:1309.3474] [INSPIRE].

  47. L. Blanchet and T. Damour, Postnewtonian Generation of Gravitational Waves, Ann. Inst. H. Poincare Phys. Theor. 50 (1989) 377 [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  48. B. Kol and M. Smolkin, Non-Relativistic Gravitation: From Newton to Einstein and Back, Class. Quant. Grav. 25 (2008) 145011 [arXiv:0712.4116] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  49. B. Kol and M. Smolkin, Classical Effective Field Theory and Caged Black Holes, Phys. Rev. D 77 (2008) 064033 [arXiv:0712.2822] [INSPIRE].

  50. J.B. Gilmore and A. Ross, Effective field theory calculation of second post-Newtonian binary dynamics, Phys. Rev. D 78 (2008) 124021 [arXiv:0810.1328] [INSPIRE].

    ADS  Article  Google Scholar 

  51. J. Blümlein, A. Maier, P. Marquard and G. Schäfer, The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions, arXiv:2010.13672 [INSPIRE].

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Authors and Affiliations

  1. Département de Physique Théorique and Centre for Astroparticle Physics, Université de Genève, CH-1211, Geneva, Switzerland

    Stefano Foffa

  2. International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal, RN, 59078-970, Brazil

    Riccardo Sturani

  3. Instituto de Física Corpuscular, Universitat de València, Consejo Superior de Investigaciones Científicas, Parc Científic, E-46980, Paterna, Valencia, Spain

    William J. Torres Bobadilla

  4. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805, München, Germany

    William J. Torres Bobadilla

Authors
  1. Stefano Foffa
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  2. Riccardo Sturani
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Correspondence to Stefano Foffa.

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ArXiv ePrint: 2010.13730

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Foffa, S., Sturani, R. & Torres Bobadilla, W.J. Efficient resummation of high post-Newtonian contributions to the binding energy. J. High Energ. Phys. 2021, 165 (2021). https://doi.org/10.1007/JHEP02(2021)165

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  • DOI: https://doi.org/10.1007/JHEP02(2021)165

Keywords

  • Classical Theories of Gravity
  • Black Holes
  • Effective Field Theories