1. Derive the expression of the 3-gluon vertex.
2. Calculate the colour factors of the following diagrams:
3. The square amplitude of the process [math]\displaystyle{ q\bar q\to gg }[/math] can be represented by the following classes of diagrams:
a) For each diagram, calculates the colour factor.
b) Adapt the answer for [math]\displaystyle{ e^+e^-\to\gamma\gamma }[/math] to obtain the expression of the first two diagrams as a function of s, t and u, neglecting quark and lepton masses.
c) Calculate the last diagram, which is a square.
The answer can be checked by taking m=0 in equation (8.12) of the Handbook of perturbative QCD (see references).