Conservative Binary Dynamics at Order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>α</mml:mi><mml:mn>5</mml:mn></mml:msup></mml:math> in Electrodynamics
Zvi Bern, Enrico Herrmann, Radu Roiban, Michael Ruf, Alexander V. Smirnov, Vladimir A. Smirnov, Mao Zeng
Abstract
We compute the potential-photon contributions to the classical relativistic scattering angle of two charged nonspinning bodies in electrodynamics through fifth order in the coupling. We use the scattering amplitudes framework, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. At fifth order, the result is expressed in terms of cyclotomic polylogarithms. Our calculation demonstrates the feasibility of the corresponding calculations in general relativity, including the evaluation of the encountered four-loop integrals.
Topics & Concepts
PhysicsScatteringGeneral relativityCoupling (piping)Binary numberOrder (exchange)Scattering amplitudeAmplitudeMathematical physicsQuantum mechanicsMathematicsMechanical engineeringEngineeringFinanceArithmeticEconomicsPulsars and Gravitational Waves ResearchQuantum Chromodynamics and Particle InteractionsHigh-Energy Particle Collisions Research