Impact of QED backgrounds on light-by-light scattering measurements at e⁺e⁻ and e⁻e⁻ colliders

The process of elastic scattering of photons ( γ γ → γ γ γ γ → γ γ , light-by-light scattering) has attracted significant interest in recent years as a loop-induced process sensitive to all charged particles. To date, this process has been studied through Delbrück scattering, photon splitting in the nuclear Coulomb field, and ultra-peripheral heavy-ion collisions at the LHC. Future precision measurements are anticipated at high-luminosity e⁺e⁻ e + e - colliders (SuperKEKb, FCC, CEPC, ILC, CLIC), their e⁻e⁻ e - e - options, and γ γ γ γ colliders based on the backscattering of laser photons. In this paper, we show that background QED processes severely limit the study of elastic light-by-light scattering at e⁺e⁻ e + e - colliders. For the e⁺e⁻ e + e - case, the main background arises from e⁺e⁻ e + e - annihilation into two photons within the detector acceptance after the initial electron and positron emit hard ISR photons at small angles. Since only two photons with a small total transverse momentum are registered in the detector in both cases, this process effectively mimics the γ γ → γ γ γ γ → γ γ signal with a significantly larger cross section at high invariant masses. Other relevant background QED processes for both types of collisions are also comprehensively analyzed and discussed.