= Solution
The <Yukawa interaction> has one real-scalar leg and an oriented <fermion> line at each vertex. At lowest connected order, two vertices exchange one scalar, so the diagrams are of order $\lambda^2$.
For two incoming <fermions>, there are two pairings of the outgoing <fermions>: the $t$ channel joins $p$ to $p'$ and $q$ to $q'$, with scalar momentum $p-p'$; the $u$ channel joins $p$ to $q'$ and $q$ to $p'$, with scalar momentum $p-q'$. <Fermion number conservation> excludes an annihilation channel for two particles carrying the same charge.
For an incoming <fermion> and <antiparticle>, there is a $t$-channel scalar exchange with momentum $p-p'=q'-q$ and an $s$-channel annihilation and recreation diagram with momentum $p+q=p'+q'$. Arrows on <antiparticle> lines run opposite to the direction of physical propagation. These are the four <tree scattering in Yukawa theory> diagrams shown below; all external momenta are labelled.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/iii/paper-50-yukawa-tree.png]
{title=Tree-level scalar-exchange diagrams for fermion–fermion and fermion–antifermion scattering; incoming states on the left}
The crossing in the $u$-channel drawing is not a vertex. Dashed internal lines are the <real scalar field>; solid arrows show fermion-number flow.
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