The One-loop QCD Corrections for gamma^* to q qbar gg

Abstract

We compute the one-loop QCD amplitudes for the decay of an off-shell vector boson with vector couplings into a quark-antiquark pair accompanied by two gluons keeping, for the first time, all orders in the number of colours. Together with previous work this completes the calculation of the necessary one-loop amplitudes needed for the calculation of the next-to-leading order O(alpha_s^3) corrections to four jet production in electron-positron annihilation, the production of a gauge boson accompanied by two jets in hadron-hadron collisions and three jet production in deep inelastic scattering.

Figures (3)

• Figure 1: The classes of Feynman diagrams relevant for the function ${\cal A}^{(1)}_A(3,4)$. Reading clockwise round the diagram and starting from the quark ($p_1$) at the top, we encounter gluon ($p_3$) before gluon ($p_4$) and end at antiquark ($p_2$). The solid circle indicates the possible positions for attaching the off-shell photon to the quark-antiquark pair. Diagrams (a), taken with both permutations of gluons 3 and 4, contribute to the piece ${\cal L}_A$ while the permutation shown in (a)+(b) gives the contribution to ${\cal L}_A(3,4)$. Diagrams with self-energy corrections on the external lines are zero in dimensional regularisation and have been omitted.
• Figure 2: The classes of Feynman diagrams relevant for the function ${\cal A}^{(1)}_B(3,4)$ Reading clockwise round the diagram and starting from the quark ($p_1$) at the top, we encounter gluon ($p_3$) before gluon ($p_4$) and end at antiquark ($p_2$). The solid circle indicates the possible positions for attaching the off-shell photon to the quark-antiquark pair. Diagrams (a), taken with both permutations of gluons 3 and 4, contribute to the piece ${\cal L}_B$ while the permutation shown in (a)+(b) gives the contribution to ${\cal L}_B(3,4)$.
• Figure 3: The classes of Feynman diagrams relevant for the function ${\cal A}^{(1)}_C$ when taken with both permutations of the gluons. Reading clockwise round the diagram and starting from the quark ($p_1$) at the top, we encounter gluon ($p_3$) before gluon ($p_4$) and end at antiquark ($p_2$). The solid circle indicates the possible positions for attaching the off-shell photon to the quark-antiquark pair.