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Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian

Stefano Foffa, Riccardo Sturani

Abstract

Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for non-spinning compact objects. Following the standard procedure, the exchange of gravitational interaction is integrated out to obtain a systematic expansion in terms of Feynman graphs. Building on this result and on previously obtained ones, we are able to write the local-in-time regularized Lagrangian at fourth post-Newtonian order, which is in agreement with results previously computed with other methods.

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian

Abstract

Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for non-spinning compact objects. Following the standard procedure, the exchange of gravitational interaction is integrated out to obtain a systematic expansion in terms of Feynman graphs. Building on this result and on previously obtained ones, we are able to write the local-in-time regularized Lagrangian at fourth post-Newtonian order, which is in agreement with results previously computed with other methods.

Paper Structure

This paper contains 17 sections, 47 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Method
  3. Results of diagram computation
  4. The 4PN ${\bm G^3}$ sector
  5. The 4PN ${\bm G^4}$ and ${\bm G^5}$ sectors
  6. The 3PN sector
  7. The regularized 3PN and 4PN Lagrangian
  8. ${\cal L}_{poles}$
  9. ${\cal L}^{(3PN)}_{fin} + {\cal L}^{(4PN)}_{fin}$
  10. Conclusions
  11. Fundamental integrals
  12. Tail terms
  13. Explicit expression of ${\cal L}_{poles}$
  14. Results of double zero tricks
  15. From 2PN
  16. ...and 2 more sections

Figures (2)

  • Figure 1: 2-loop master integrals in eq. (\ref{['eq:2loopMI']}).
  • Figure 2: 3-loop master integrals in eq. (\ref{['eq:3loopMI']}).