TwoPhoton Mechanism of Particle Production by HighEnergy Colliding Beams
Abstract
We report on the calculation of the cross sections for the production of positivechargeconjugation states such as π^{0}, η, e^{+}e^{}, μ^{+}μ^{}, and π^{+}π^{} by a twophoton mechanism in e^{}e^{+} and e^{}e^{} collisions. We give the precise relationship of the process e+e>e+e+X (X is any C=+ state) to the corresponding twophoton annihilation process γ+γ>X, as well as a careful derivation of the equivalentphoton approximation. In the case of the π^{0} production, we have found that, for the beam energy E in the 13 GeV range, the exact total cross section is 2030% larger than the one calculated previously in the equivalentphoton approximation. However, the introduction of form factors cuts down the exact total cross section, reducing it to within 10% of the equivalentphotonapproximation result. For η production the agreement is even better. Thus it appears that the use of the equivalentphoton 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 equivalentphoton 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 4050% 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.
 Publication:

Physical Review D
 Pub Date:
 September 1971
 DOI:
 10.1103/PhysRevD.4.1532
 Bibcode:
 1971PhRvD...4.1532B