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.