An experiment of X-ray photon-photon elastic scattering with a Laue-case beam collider

We report a search for photon-photon elastic scattering in vacuum in the X-ray region at an energy in the center of mass system of \omega_{cms} =6.5 keV for which the QED cross section is \sigma_{QED} =2.5 \times 10^{-47} m^2. An X-ray beam provided by the SACLA X-ray Free Electron Laser is split and the two beamlets are made to collide at right angle, with a total integrated luminosity of (1.24 \pm 0.08) \times 10^{28} m^{-2}. No signal X rays from the elastic scattering that satisfy the correlation between energy and scattering angle were detected. We obtain a 95% C.L. upper limit for the scattering cross section of 1.9 \times 10^{-27} m^2 at \omega_{cms}=6.5 keV. The upper limit is the lowest upper limit obtained so far by keV experiments.