Bounding elastic photon-photon scattering at sqrt s approx 1\,MeV using a laser-plasma platform

We report on a direct search for elastic photon-photon scattering using x-ray and $\gamma$ photons from a laser-plasma based experiment. A gamma photon beam produced by a laser wakefield accelerator provided a broadband gamma spectrum extending to above $E_\gamma = 200$ MeV. These were collided with a dense x-ray field produced by the emission from a laser heated germanium foil at $E_x \approx 1.4$ keV, corresponding to an invariant mass of $\sqrt{s} = 1.22 \pm 0.22$ MeV. In these asymmetric collisions elastic scattering removes one x-ray and one high-energy $\gamma$ photon and outputs two lower energy $\gamma$ photons. No changes in the $\gamma$ photon spectrum were observed as a result of the collisions allowing us to place a 95% upper bound on the cross section of $1.5 \times 10^{15}\,\mu$b. Although far from the QED prediction, this represents the lowest upper limit obtained so far for $\sqrt{s} \lesssim 1$ MeV.