Polarization effects in light-by-light scattering: Euler-Heisenberg versus Born-Infeld

The angular dependence of the differential cross section of unpolarized light-by-light scattering summed over final polarizations is the same in any low-energy effective theory of quantum electrodynamics and also in Born-Infeld electrodynamics. In this paper we derive general expressions for polarization-dependent low-energy scattering amplitudes, including a hypothetical parity-violating situation. These are evaluated for quantum electrodynamics with charged scalar or spinor particles, which give strikingly different polarization effects. Ordinary quantum electrodynamics is found to exhibit rather intricate polarization patterns for linear polarizations, whereas supersymmetric quantum electrodynamics and Born-Infeld electrodynamics give particularly simple forms.