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

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