Factorization of photon induced processes in ultra-peripheral heavy ion collisions

In this study, we investigate photon-photon scattering in ultra-peripheral heavy ion collisions (UPCs). We start by deriving an effective Lagrangian from first principles and then apply factorization techniques from Soft-Collinear effective theory (SCET). This approach allows us to decompose the photon-photon scattering cross-section into two primary factors: the generalized transverse momentum distributions (GTMDs) and the hard scattering amplitude. We further analyze the emission of soft photons by final state leptons, incorporating a soft function into the cross section through an evolution method. Our analysis yields detailed predictions for observable angular correlations among the final state leptons. Specifically, we calculate the angular correlations characterized by the azimuthal parameters $〈\cos 2\varphi 〉$ and $〈\cos 4\varphi 〉$, highlighting the influence of initial photons polarization and recoil effects from final state soft photons.