Testing helicity dependent $γγ\rightarrowγγ$ scattering in the region of MeV
Light-by-light scatterings contain rich information on the photon coupling to virtual and real particle states. In the context of quantum electrodynamics (QED), photons can couple to a virtual $e^+e^-$ pair. Photons may also couple to known resonance states in the context of quantum chromodyanmics and electroweak dynamics in higher energy domains and possibly couple to unknown resonance states beyond the starndard model. The perturbative QED calculations manifestly predict the maximized cross section at the MeV scale, however, any example of the exact real-photon - real-photon scattering has not been observed hitherto. Hence, we propose the direct measurement with the maximized cross-section at the center-of-mass system energy of 1-2 MeV to establish the firm footing at the MeV scale. Given currently state-of-the-art high power lasers, the helicity dependent elastic scattering may be observed at a reasonable rate, if a photon-photon collider exploiting $γ$-rays generated by the inverse nonlinear Compton process with electrons delivered from laser-plasma accelerators (LPA) are properly designed. We show that such verification is feasible in a table-top scale collider which may be an unprecedented breakthrough in particle accelerators for basic physics research in contrast to energy frontier colliders.