Fundamental constants from photon-photon scattering in three-beam collisions

Direct measurement of the elastic scattering of real photons on an electromagnetic field would allow the fundamental low-energy constants of quantum electrodynamics to be experimentally determined. We show that scenarios involving the collision of three laser beams have several advantages over conventional two-beam scenarios. The kinematics of a three-beam collision allows for a higher signal-to-background ratio in the detection region, without the need for polarimetry, and separates out contributions from different orders of photon scattering. A planar configuration of colliding a photon beam from an x-ray free-electron laser with two optical beams is studied in detail. We show that measurements of elastic photon scattering and vacuum birefringence are possible with currently available technology.