Spin Effects in Long Range Electromagnetic Scattering
Barry R. Holstein, Andreas Ross
TL;DR
By employing effective field theory, the paper isolates the leading long-range contributions to electromagnetic scattering beyond one-photon exchange, distinguishing classical $1/\sqrt{-q^2}$ and quantum $\log(-q^2)$ nonanalytic terms. The results show a universal long-range structure across spin configurations and yield a leading potential form $V(r) = \frac{\alpha}{r} \left(1 + A_C \frac{\alpha}{mr} + A_Q \, \hbar \frac{\alpha}{(mr)^2} \right)$, with explicit spin-0, spin-1/2, and spin-1 cases exhibiting spin-independent, spin-orbit, and potentially spin-spin interactions. The analysis ties in with previous dispersive calculations and gravitational scattering analogies, providing a coherent EFT framework for long-distance electromagnetic corrections and informing high-precision form-factor extractions and polarization measurements.
Abstract
We analyze the electromagnetic scattering of massive particles with and without spin and, using the techniques of effective field theory, we isolate the leading long distance effects beyond one photon exchange, both classical and quantum mechanical. Spin-independent and spin-dependent effects are isolated and shown to have a universal structure.