Radiative corrections in photon-photon collisions induced bye+e−ore±e±processes

In this work we present an evaluation of radiative corrections to order ${\alpha }^5$ pertaining to $\gamma -\gamma$ collision experiments performed with an $e^{\pm }{e}^{\pm }$ storage ring in which the electrons scattered are detected at small angle. We check that the infrared divergences originating from elastic corrections are canceled due to opposite divergences from real-photon bremsstrahlung. Numerical results for given experimental conditions allow one to compare the various contributions to radiative corrections in processes such as $\mathrm{ee}\to \mathrm{eeX}$ with $X=e^{+}{e}^{-},{\mu }^{+}{\mu }^{-},{\pi }^{+}{\pi }^{-}$