Transverse momentum distribution of lepton-pairs in Drell-Yan process in an asymptotically free scalar field theory

The transverse momentum dependence of the parton distribution function and the Drell-Yan cross section is studied in detail in the asymptotically free scalar field theory in six dimensions. In the context of the renormalization group approach of Collins, particular attention is devoted to the transition between the small q_T formula (due to multe-quanta effects) and the large q_T formula (due to single hard-quantum emission). The calculation represents a case study of the application of the renormalization group method and provides a guide to the corresponding study in QCD.