CANCELLATION OF INFRARED AND COLLINEAR DIVERGENCES IN ONE-LOOP CORRECTIONS TO THE PHYSICAL CROSS-SECTION OF ANY QCD PROCESS

Infrared and collinear divergences arising in one-loop corrections are extracted for any QCD process. The temporal gauge (A0 = 0) proves to be the most convenient for this purpose. The divergences are expressed in terms of In λ, In η and In η λ where λ stands for the infrared and ν for the angular cutoff in Feynman integrals. In the temporal gauge, collinear (-αs ln η) and dilogarithmic (-αs ln η) div η) divergences are connected to the external lines only and are factorized in an extremely simple way. Pure infrared (∼αs ln λ) divergences are also computed for any QCD process. All the divergences are shown to cancel out from the transition rates integrated over the final and initial degenerate states, with only ln ε and ln δ remaining (ε, δ are the energy and the angular resolutions respectively). Infrared stable multijet production cross sections are considered and a generalization of the Sterman-Weinberg formula for any process is derived. The general formula is applied to the particular processes e+e- → qqγ, e+e- → qqγs and Γ → 3γs. The gluon corrections to Γ → 3γs decay are shown to be large, so that the three-jet structure will be hardly observed in this process. © 1979.