Long Distance Effects in Mixed Electromagnetic-Gravitational Scattering
Barry R. Holstein, Andreas Ross
TL;DR
The paper addresses inconsistent results for long-range corrections in mixed electromagnetic-gravitational scattering at one-loop order $O(G \alpha)$ across different spins. It employs effective field theory to isolate nonanalytic momentum-transfer terms in the amplitude, separating classical $1/\sqrt{-q^2}$ and quantum $\log(-q^2)$ contributions arising from photon-graviton loops. The authors compute the spin-0--spin-0, spin-0--spin-1/2, spin-0--spin-1, and spin-1/2--spin-1/2 scattering amplitudes, presenting spin-independent and spin-dependent pieces and resolving previous disagreements with results of Bjerrum-Bohr, Butt, and Faller, in line with universality expectations from Holstein and Ross. The findings provide a consistent, spin-universal description of the $O(G \alpha)$ potential, clarifying the long-range structure of mixed EM-gravitational interactions and informing high-precision scattering analyses.
Abstract
Using the methods of effective field theory we examine long range effects in mixed electromagnetic-gravitational scattering. Recent calculations which have yielded differing results for such effects are examined and corrected. We consider various spin configurations of the scattered particles and find that universality with respect to spin-dependence is obtained in agreement with expectations.