Vacuum birefringence by Compton backscattering through a strong field

We propose a novel scheme to measure nonlinear effects in electrodynamics arising from QED corrections. Our theoretical starting point is the Heisenberg-Euler-Schwinger effective Lagrangian which predicts that a vacuum with a strong static electromagnetic field turns birefringent. We propose to employ a pulsed laser to create Compton backscattered photons off a high energy electron beam. These photons will pass through a strong static magnetic field, which according to the QED prediction changes the state of polarization of the radiation—an effect proportional to the photon energy. This change will be measured by using an aligned single crystal, since a large difference in the pair production cross sections at high energies can be achieved with proper orientation of the crystal. As an example we will consider the machine, LHeC, under consideration at CERN as the source of these electrons, and an LHC dipole magnet as the source of the strong static magnetic field. In the proposed experimental setup the birefringence effect will be manifested in a difference in the number of pairs created in the polarizer crystal as the initial laser light has a varying state of polarization, achieved with a rotating quarter wave plate. This will be seen as a clear peak in the Fourier transform spectrum of the pair-production rate signal, which can be obtained with 3 hours of measurement. We also comment on the sensitivity of the experiment, to the existence of an axion, a hypothetical spin-0 particle that couples to two photons.