Meson--photon transition form factors and resonance cross-sections in e^+ e^- collisions

Abstract

Meson--photon--photon transition form factors for S-, P-, and D-wave states are calculated, the meson being treated as a non-relativistic heavy-quark--antiquark pair. The full dependence on both photon virtualities is included. Cross-section formulas for charge-conjugation even mesons with J^P = 0^-, 0^+, 1^+, 2^+, and 2^- in electron--positron collisions are presented and numerical results for LEP energies are given. In particular, we find two-photon event rates for χ_{\rc 1}, η_{\rc}(2S), and η_{\rb}(1S) within reach of LEP. With minor modifications to incorporate SU(3)-flavour breaking we estimate rates for 18 light mesons as well, based on the observation that their two-photon decay widths agree remarkably well with measured data. Finally we point out that e^+ e^- cross sections for 1^+ states do not vanish at low Q^2, the Landau--Yang suppression factors of the two-photon cross sections being compensated by the photon propagators.