Non-perturbative vacuum-polarization effects in proton-laser collisions

In the collision of a high-energy proton beam and a strong laser field, merging of the laser photons can occur due to the polarization of vacuum. The probability of photon merging is calculated by accounting exactly for the laser field and presents a highly non-perturbative dependence on the laser intensity and frequency. It is shown that the non-perturbative vacuum-polarization effects can be experimentally measured by combining the next-generation of table-top petawatt lasers with presently available proton accelerators.