Two-Photon Mechanism of Particle Production by High-Energy Colliding Beams

We report on the calculation of the cross sections for the production of positive-charge-conjugation states such as π⁰, η, e⁺e^-, μ⁺μ^-, and π⁺π^- by a two-photon mechanism in e^-e⁺ and e^-e^- collisions. We give the precise relationship of the process e+e→e+e+X (X isany C=+ state) to the corresponding two-photon annihilation process γ+γ→X, as well as a careful derivation of the equivalent-photon approximation. In the case of the π⁰ production, we have found that, for the beam energy E in the 1-3 GeV range, the exact total cross section is 20-30% larger than the one calculated previously in the equivalent-photon approximation. However, the introduction of form factors cuts down the exact total cross section, reducing it to within 10% of the equivalent-photon-approximation result. For η production the agreement is even better. Thus it appears that the use of the equivalent-photon approximation is justified in most cases. We discuss detailed angular distributions in this approximation for the case of π⁺π^- production. One important problem which cannot be adequately studied in the equivalent-photon approximation is the degree of noncoplanarity of the π⁺π^- (and the μ⁺μ^-) pair. We have studied this problem using the exact formula and found that, for $E=1$ GeV, typically 40-50% of pion pairs will be produced with the noncoplanarity angle greater than 12^∘{}. We discuss the general structure of the γ+γ→π⁺+π^- amplitude as well as a simple model incorporating the σ meson. We also give a rough estimate of multihadron production cross sections.