Comment on the Experimental Investigation of Photon - Photon Collisions in Electron - Positron Storage Rings

Continuing our calculations on photon-photon collisions in electron-positron storage rings, i.e., reactions of the type $e^{-}{e}^{+}\to e^{-}{e}^{+}{A}^{-}{A}^{+}$ (where $A=e,\mu ,\pi ,K,\dots$), we now introduce realistic experimental conditions, in particular two cutoff parameters: a minimal emission angle (${\psi }_{min}$) with respect to the beam axis for the particles $A^{\pm }$ to be produced, and a minimal relative energy loss (${\chi }_{min}$) for the outgoing electron and positron (to be detected practically in their forward directions). Taking realistic values for ${\psi }_{min}$ and ${\chi }_{min}$, their effect on the invariant mass spectrum of the pair $A^{-}{A}^{+}$ and on the integrated cross section is shown. In particular, the modification of the energy behavior, due to these cutoffs, is exhibited. In spite of the drastic character of the restrictions considered, it is shown that fairly high counting rates may still be expected (for $A=e,\mu ,\pi$) in the four-fold coincidence experiments suggested, with electron-positron storage rings of the next generation (beam energy 2-3 GeV, luminosity ∼ ${10}^{32}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$).