Towards a direct measurement of the quantum vacuum Lagrangian coupling coefficients using two counter propagating super-intense laser pulses

In this paper we will show that photon-photon collision experiments using extreme lasers can provide measurable effects giving fundamental information about the essence of QED, its Lagrangian. A possible scenario with two counterpropagating ultraintense lasers for an experiment to detect scattering between optical photons is analyzed. We discuss the importance of the pulse widths and waists, the best scenario for overlapping the beams and signal detection, as well as ways to distinguish the signal from the noise. This would need a high-precision measurement, with control of temporal jitter and noise. We conclude that such experiment is barely feasible at 10^{23} W/cm^2 and very promising at 10^{24} W/cm^2