A nonlinear interaction between photons is observed in a process that involves charge sources. To observe this process in a vacuum, there are a growing number of theoretical and experimental studies. This process may contain exotic contribution from new physics beyond the Standard Model of particle physics, and is probed by experiments using a high-power laser or a high-field magnet, and more recently using an X-ray Free-Electron Laser (XFEL). Here, we review the present status of our experiments testing various vacuum processes. We describe four experiments with a focus on those using an XFEL: (i) photon-photon scattering in the x-ray region, (ii) laser-induced birefringence and diffraction of x rays, (iii) vacuum birefringence induced by a high-field magnet, and (iv) a dedicated search for axion-like particles using the magnet and x rays.
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