QCD effects on e+e- → μ+μ-X

QCD effects on the process e+e- → #betta#*(q2) → #betta#*(q tilde2)X → μ+μ-X are calculated. In the non-resonant (continuum) region for q tilde2, there exists a kinematical region where the virtual photon with momentum q tilde is dominantly emitted directly from the quark. Fragmentation functions of the quark and the gluon to the photon depend not only on q2 but also on q tilde2 and more detailed test of QCD effects can be made in this process than in the case of the real photon production. The fragmentation functions are calculated and their dependence on q2, q tilde2 and #betta# is predicted. Some possible background processes to the direct emission are discussed. (author)