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Description
Quantum field theory predicts the vacuum to exhibit a non-linear response to strong electro-magnetic fields [1]. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory [2]. Macroscopic electromagnetic fields available in the laboratory fulfill $\left\{ \left|\overrightarrow{E}\right|,c\left|\overrightarrow{B}\right|\right\} \ll E_{S}$, with $E_{S}=m^{2}c^{3}/\left(e\hbar\right)$ set by QED parameters: the electron mass m and elementary charge e. If these fields vary on scales much larger than the Compton wavelength of the electron $\lambda_{C}=\hbar/\left(mc\right)\simeq1.3\times10^{18}m$, their leading interactions are governed by $\left(c=\hbar=1\right)$
$\mathcal{L}_{int}\simeq\frac{m^{4}}{1440\pi^{2}}\left[a\left(\frac{\overrightarrow{B}^{2}-\overrightarrow{E}^{2}}{E_{S}^{2}}\right)^{2}+b\left(\frac{2\overrightarrow{B}\cdot\overrightarrow{E}}{E_{S}^{2}}\right)^{2}\right] $.
The constants a and b control the strength of the four-field couplings. QED predicts these to have a series expansion in $\alpha=e^{2}/\left(4\pi\right)\simeq1/137$ and read [1,3]
$a=4\left(1+\frac{40}{9}\frac{\alpha}{\pi}+\ldots\right)$, $b=7\left(1+\frac{1315}{252}\frac{\alpha}{\pi}+\ldots\right)$.
We present proof of concept and detailed theoretical analysis of an experimental setup for precision measurements of the quantum vacuum signal generated by the collision of a brilliant x-ray probe with a high-intensity pump laser [4]. Our proof-of-concept measurements show that the background can be efficiently suppressed by many orders of magnitude. This should facilitate a detection of both polarization components (⊥, ∥) of non-linear vacuum response and thereby provide direct access to the low-energy constants a and b governing light-by-light scattering.
[1] W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
[2] A. Fedotov, et al.Phys. Rept. 1010, 1-138 (2023).
[3] V. Ritus, J. Exp. Theor. Phys. 42, 774 (1975).
[4] F. Karbstein, D. Ullmann, E. A. Mosman and M. Zepf, Phys. Rev. Lett. 129, 061802 (2022).
