Four Pion Final States with Tagged Photons at Electron Positron Colliders

A Monte Carlo generator has been constructed to simulate the reaction e^+e^- \to \gamma + 4 \pi, where the photon is assumed to be observed in the detector. Isospin relations between the amplitudes governing tau decays into four pions and electron positron annihilation into four pions respectively have been found which allow to determine all four modes after the amplitude for the \pi^+\pi^-2\pi^0 channel has been fixed. The kinematic breaking of these isospin relations as a consequence of the \pi^- -- \pi^0 mass difference has also been investigated. The program is constructed in analogy to an earlier one simulating e^+e^- \to \gamma + 2 \pi. However, it does not include final state radiation from the charged pions. Additional collinear photon radiation has been incorporated with the technique of structure functions. Predictions are presented for cms energies of 1GeV, 3GeV and 10GeV, corresponding to the energies of DAPHNE, BEBC and of B-meson factories. Using this program it is demonstrated that, even after applying realistic cuts, the event rates are sufficiently high to allow for a precise measurement of R(Q^2) in the region of Q between approximately 1GeV and 2.5GeV. The model predictions are compared to recent data from electron positron colliders and agreement is obtained within the relatively large errors.