## 2 Probing the Vacuum Process
### Elastic Scattering by the Collision of Two X-ray Pulses  
This section reviews our experiments at SACLA that provide the first limits on the QED cross-section of photon-photon scattering (\(\sigma_{\gamma\gamma}\)) in the X-ray region [19,20]. Before the experiments, the scattering was tested by using optical lasers [21]. However, the cross-section is suppressed by the sixth power of the ratio \(\hbar\omega/m_{\mathrm{e}}c^{2}\), where \(\omega\) is the photon energy and \(m_{\mathrm{e}}\) the electron mass [22,23]. Therefore, a significant enhancement can be obtained by using high-energy X-ray photons. It is not an easy task to collide X-ray pulses if they are delivered as two distinct beams. Thus, we developed a new scheme to divide a single beam into two and then to collide them. This scheme applies a technology established for an X-ray interferometer. A schematic of the beam splitter is shown in Figure 3a. A beam is split into two coherent beams--one is the transmitted beam (T) and the other is the reflected one (R)--by a 0.6 mm-thick blade of Si(440) crystal when the lattice plane matches a diffraction angle of \(\theta_{\mathrm{B}}=36^{\circ}\)[24]. A similar process occurs at the second blade, creating four beams after the two blades. The TR and RR beams collide obliquely with a crossing angle of \(2\theta_{\mathrm{B}}\), and the two-photon system is boosted along \(\theta_{\mathrm{B}}\). The change of wave vectors in the center-of-mass system causes energy unbalance of the pairs observed in the laboratory frame. This is an example of a kinematically-induced frequency change occurring in oblique collisions, in contrast to one caused by optical nonlinearities such as four-wave mixing [25]. In this way, the diffraction condition itself ensures the geometrical equivalence of the beam paths split by the symmetric Laue reflection [26]. A magnified view of the beam-collision chamber is shown in Figure 3b. The splitter is installed in the chamber and fixed to a rotary feedthrough connected to a goniometer. The intensities of the two beams are monitored pulse-by-pulse by silicon PIN photodiodes (PDs). One of the paired signal photons--the forward-scattered one--has higher energy than the original photons  
Figure 3: (**a**) Four beams after the two blades of the silicon beam splitter. (**b**) Magnified view of the beam-collision chamber. Adapted from Reference [19]. PD: photodiode; R: reflected beam; T: transmitted beam. (\(\omega_{0}=11\) keV), and is easily separated from backgrounds. To select forward-scattered photons, a collimator flange with a conically tapered hole is placed after the collision point. The full angle of the cone is \(25^{\circ}\), defining the signal energy region from 18.1 keV to 19.9 keV. The first experiment was performed on 23 and 24 July 2013 at SACLA with a total injection of \(6.5\times 10^{5}\) pulses. A timing cut was applied to select events within \(\pm 1\) us of the arrival of X-ray pulses. Figure 4(left) shows the energy spectrum after the cut. An elastic peak from stray X-rays is observed around \(\omega_{0}\) as well as some events at \(2\omega_{0}\) due to the pileup of two photons. No events are observed in the signal region, and the resulting limit on \(\sigma_{\gamma\gamma}\) is shown in Figure 4(right) with other limits. After the first experiment, we upgraded it in the second experiment carried out in 2015 [20]. The main improvements are in (i) the efficiency of the beam splitter, (ii) the performance of the XFEL, and (iii) the statistical gain by larger measurement time. The total improvement from the first result is by three orders of magnitude, and gives the most stringent limit in the X-ray region, which still needs to be gained by 20 orders of magnitude to reach the QED cross section. On the basis of these experiences, we are planning to further improve the sensitivity in the next phase. The first approach is to apply a similar splitter in the Bragg case as seen in Reference [27].