Four pion final states with tagged photons at electron positron colliders

Abstract.

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. Only initial state radiation is considered. Additional collinear photon radiation has been incorporated with the technique of structure functions. Predictions are presented for CMS energies of 1 GeV, 3 GeV and 10 GeV, corresponding to the energies of DA$\Phi$NE, BEBC and of B-meson factories. The event rates are sufficiently high to allow for a precise measurement of $R(Q^2)$ in the region of Q between approximately 1 GeV and 2.5 GeV. For the construction of the program we employ isospin relations between the amplitudes governing $\tau$ decays into four pions and electron positron annihilation into four pions. Estimates of the kinematic breaking of these isospin relations as a consequence of the $\pi^-$–$\pi^0$ mass difference are given.