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Conservative Binary Dynamics at Order α^{5} in Electrodynamics.

Zvi Bern1, Enrico Herrmann1, Radu Roiban2

  • 1Mani L. Bhaumik Institute for Theoretical Physics, <a href="https://ror.org/046rm7j60">University of California at Los Angeles</a>, Los Angeles, California 90095, USA.

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Summary
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Researchers calculated potential-photon contributions to relativistic scattering angles for charged particles. This fifth-order calculation in electrodynamics advances precision in gravitational wave and black hole merger predictions.

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Area of Science:

  • Theoretical Physics
  • Quantum Electrodynamics
  • Gravitational Wave Physics

Background:

  • Precise calculations of relativistic scattering are crucial for understanding gravitational wave signals from compact object mergers.
  • Previous calculations were limited in order, necessitating higher-order contributions for improved accuracy.

Purpose of the Study:

  • To compute potential-photon contributions to the classical relativistic scattering angle of two charged nonspinning bodies.
  • To achieve this computation through fifth order in the coupling constant within electrodynamics.
  • To demonstrate the feasibility of such calculations for general relativity.

Main Methods:

  • Utilized the scattering amplitudes framework.
  • Employed effective field theory techniques.
  • Applied multiloop integration methods, including integration by parts and differential equations.

Main Results:

  • Successfully computed potential-photon contributions to the relativistic scattering angle to fifth order.
  • The fifth-order result is expressed in terms of cyclotomic polylogarithms.
  • Demonstrated the feasibility of evaluating complex four-loop integrals relevant to general relativity.

Conclusions:

  • The study provides a significant advancement in precision calculations for relativistic scattering.
  • The methods developed are applicable to more complex scenarios in general relativity.
  • This work paves the way for more accurate modeling of astrophysical phenomena like black hole mergers.