Double equivalent-photon approximation including radiative corrections for photon-photon collision experiments without electron tagging

It is shown that, in first approximation, radiative corrections in photon-photon collision experiments without electron tagging can be estimated by using a double equivalent-photon approximation of the same type as (but, of course, analytically much more complicated than) that used for computation of $\gamma \gamma$ cross sections without radiative corrections. It is obvious that, in such an approximation, radiative corrections—for a given beam energy $E_0$ and a given invariant mass $M$ produced—become independent of the specific process $\gamma \gamma \to X$ considered. The invariant-mass spectrum, corrected for radiation, will be written in the general form $\frac{d{\sigma }^{\mathrm{corr}}}{\mathrm{dM}}=(1+\delta )\frac{d{\sigma }^0}{\mathrm{dM}}$ where $\frac{d{\sigma }^0}{\mathrm{dM}}$ is the uncorrected spectrum. Values obtained for $\delta$ at typical beam energies $E_0=1.5, 3, 15, \mathrm{and} 70$ GeV, and for $\frac{M}{E_0}$ ranging between 0.1 and 0.6, are systematically of the order of less than ± 1%.