R5b

1. Calculate the colour factors of the following diagrams:
2. 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) Calculates 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).

d) Calculate the interference terms (3rd, 4th diagrams). Are there other similar interference terms?

e) GIve the expression of the differential cross section as a function of the solid angle, [math]\displaystyle{ d\sigma/d\Omega }[/math].