= Solution
{c}
There are three <tree-level Feynman diagrams>: two ordered fermion-exchange diagrams and one <s-channel> <gauge boson> exchange diagram. Write the outgoing labels as $(k_1,a,\mu)$ and $(k_2,b,\nu)$.
\Image[/past-exam-of-the-advanced-quantum-field-theory-for-particle-physics-course-of-the-university-of-oxford/2024-fermion-annihilation-diagrams.png]
{title=Original <tree-level Feynman diagrams> for <fermion> and <antifermion> annihilation into two non-Abelian <gauge bosons>: two ordered exchanges and the three-boson annihilation channel}
Following the <fermion flow> from $u(p_1)$ to $\bar v(p_2)$, the first diagram emits boson 1 and then boson 2; its internal <four-momentum> is $r_t=p_1-k_1$ and its ordered colour factor is $t^bt^a$. The second emits boson 2 and then boson 1, giving $r_u=p_1-k_2$ and $t^at^b$. The third annihilates into one virtual <gauge boson> of <four-momentum> $q=p_1+p_2=k_1+k_2$ and uses the three-boson <interaction vertex>. There is no two-fermion two-boson contact <interaction vertex> for the minimally coupled <Dirac field>, and no tree ghost contribution with these external states.
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