On production of gluon jets in e+e- collisions

The processes with the production of gluons in the e+e--collisions in the lowest order of the perturbation theory with respect to electromagnetic α and strong αsub(s) coupling constants have been studied. Production of gluons occurs due to generation and subsequent annihilation of a quark-antiquark pair in an intermediate state. Production of three gluons in a one-photon channel at the e+e- annihilation is considered. For comparison presented is the cross-section of creation of a state of a quark-antiquark pair with an extra gluon in the annihilation channel. Production of two gluons in the channel of scattering (two-photon mechanism) and formation of a quark-antiquark pair in a similar manner, scattered at large angles in the C-system are studied. Helical amplitudes of the light scattering by light written out in the form convenient for this problem are given. These helical amplitudes are used to calculate the contribution of their imaginary part corresponding to an intermediate state with a e+e--pair to t.he cross-section of the three photon production. This result is in agreement with the Ore-Powell formula for the cross section of the nonrelativistic e+e--pair annihilation to three photons