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

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.