THE ONE-LOOP QCD CORRECTIONS FOR GAMMA-ASTERISK-]Q(Q)OVER-BAR-Q(Q)OVER-BAR

We present the first calculation of the one-loop QCD corrections for t he decay of an off-shell vector boson with vector couplings into two p airs of quarks of equal or unequal flavours keeping all orders in the number of colours. These matrix elements are relevant for the calculat ion of the next-to-leading order O(alpha(s)(3)) corrections to four je t production in electron-positron annihilation, the production of a ga uge boson accompanied by two jets in hadron-hadron collisions and thre e jet production in deep inelastic scattering. We compute the interfer ence of one-loop and tree level Feynman diagrams, and organise the mat rix elements in terms of combinations of scalar loop integrals that ar e well behaved in the limit of vanishing Gram determinants. The result s are therefore numerically stable and ready to be implemented in next -to-leading order Monte Carlo calculations of the e(+)e(-) --> 4 jet, e(+/-)p --> e(+/-)+3 jet and p (p) over bar --> V+2 jet processes. (C) 1997 Elsevier Science B.V.