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EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity

Michele Levi, Jan Steinhoff

TL;DR

EFTofPNG introduces an open-source, Mathematica-based package for high-precision PN gravity calculations that include spins, built on an EFT framework and Feynman-calculus. It leverages xTensor and NR-field formalism to automate the generation of contractions and diagrams across a tower of scales, providing a complete pipeline from Feynman rules to gauge-invariant observables and GW templates. Version 1.0 targets the point-mass sector up to $3$PN and all spin sectors up to $4$PN (including NNLO spin terms) with two-loop accuracy, and is designed for community-driven extension. The work addresses a gap in analytic PN waveform modeling by delivering a self-contained, modular tool to support high-precision GW data analysis and waveform development.

Abstract

We present a new public package "EFTofPNG" for high precision computation in the effective field theory of post-Newtonian (PN) Gravity, including spins. We created this package in view of the timely need to publicly share automated computation tools, which integrate the various types of physics manifested in the expected increasing influx of gravitational wave (GW) data. Hence, we created a free and open source package, which is self-contained, modular, all-inclusive, and accessible to the classical Gravity community. The "EFTofPNG" Mathematica package also uses the power of the "xTensor" package, suited for complicate tensor computation, where our coding also strategically approaches the generic generation of Feynman contractions, which is universal to all perturbation theories in physics, by efficiently treating n-point functions as tensors of rank n. The package currently contains four independent units, which serve as subsidiaries to the main one. Its final unit serves as a pipeline chain for the obtainment of the final GW templates, and provides the full computation of all derivatives and gauge invariant physical observables of interest. The upcoming "EFTofPNG" package version 1.0 should cover the point mass sector, and all the spin sectors, up to the fourth PN order, and the two-loop level. We expect and strongly encourage public development of the package to improve its efficiency, and to extend it to further PN sectors, and observables useful for the waveform modeling.

EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity

TL;DR

EFTofPNG introduces an open-source, Mathematica-based package for high-precision PN gravity calculations that include spins, built on an EFT framework and Feynman-calculus. It leverages xTensor and NR-field formalism to automate the generation of contractions and diagrams across a tower of scales, providing a complete pipeline from Feynman rules to gauge-invariant observables and GW templates. Version 1.0 targets the point-mass sector up to PN and all spin sectors up to PN (including NNLO spin terms) with two-loop accuracy, and is designed for community-driven extension. The work addresses a gap in analytic PN waveform modeling by delivering a self-contained, modular tool to support high-precision GW data analysis and waveform development.

Abstract

We present a new public package "EFTofPNG" for high precision computation in the effective field theory of post-Newtonian (PN) Gravity, including spins. We created this package in view of the timely need to publicly share automated computation tools, which integrate the various types of physics manifested in the expected increasing influx of gravitational wave (GW) data. Hence, we created a free and open source package, which is self-contained, modular, all-inclusive, and accessible to the classical Gravity community. The "EFTofPNG" Mathematica package also uses the power of the "xTensor" package, suited for complicate tensor computation, where our coding also strategically approaches the generic generation of Feynman contractions, which is universal to all perturbation theories in physics, by efficiently treating n-point functions as tensors of rank n. The package currently contains four independent units, which serve as subsidiaries to the main one. Its final unit serves as a pipeline chain for the obtainment of the final GW templates, and provides the full computation of all derivatives and gauge invariant physical observables of interest. The upcoming "EFTofPNG" package version 1.0 should cover the point mass sector, and all the spin sectors, up to the fourth PN order, and the two-loop level. We expect and strongly encourage public development of the package to improve its efficiency, and to extend it to further PN sectors, and observables useful for the waveform modeling.

Paper Structure

This paper contains 13 sections, 9 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The EFT of PNG including spins
  3. The EFTofPNG package version 1.0
  4. Main: Evaluating the two-body effective action
  5. FeynRul: Preparing the Feynman rules.
  6. FeynGen: Processing the Feynman diagrams.
  7. FeynInteg: Handling the Feynman integration.
  8. FeynComp: Evaluating the Feynman diagrams.
  9. FeynRul: Deriving the Feynman rules
  10. FeynGen: Generating Feynman graphs
  11. NLoop: Producing loop master integrals
  12. The gauge invariant observables pipeline
  13. Conclusions

Figures (1)

  • Figure 1: Outline of the "EFTofPNG" package version 1.0. Details on the different units of the package, and the dependencies among them are given below.