Precision tests of QED and non-standard models by searching photon-photon scattering in vacuum with high power lasers

We study how to search for photon-photon scattering in vacuum at present petawatt laser facilities such as HERCULES, and test Quantum Electro dynamicsandnons tandard models like Born-Infeld theory or scenarios involving minicharged particlesor axion-like bosons. First, we compute the phase shift that is produced when anultra-intense laser beam crosses alow power beam, in the case of arbitrary polarisations. Thisresult is then used in order to design a complete test of all the parameters appearing in the low energy effective photonic Lagrangian. In fact, we propose a set of experiments that can be performed at HERCULES, eventually allowing either to detect photon-photon scattering as due to new physics, or to set new limits on there levant parameters, improving by several orders of magnitude the current constraints obtained recently by PVLAS collaboration. We also describe a multi-cross optical mechanism that can further enhance the sensitivity, enabling HERCULES to detect photon-photon scattering even at a rate as small as that predicted by QED. Finally, we discuss how these results can be improved at future exawatt facilities such as ELI, thus providing a new class of precision tests of the Standard Model and beyond