The kinematic and symmetry structure of e+e- to hadron pairs

The kinematic singularity and constraint free amplitudes for e/sup +/e /sup -/ to two particles which can have arbitrary spins are obtained in a simple closed form. The relationships of these amplitudes with the usual multipole form factors are given. It is noted that SU(6)/sub W/ and tests of ideas based on the Melosh transformation are liberated from their gamma N and pi N arena and can be confronted with arbitrary targets and excitations. The matrix elements for arbitrary meson pairs are then derived, rates are computed for pseudoscalar and vector meson production, and some tests of symmetry breaking mechanisms proposed. Extension to SU(4)(SU(8)/sub W/) broken in the masses enables estimates of charmed particle production rates to be obtained. General features of pi R final states suggest that scaling violation at small x may be connected with threshold phenomena as channels open up. A subtle difference between space-like and time-like regions is highlighted. (30 refs).