= Solution
In <phi cubed theory>, each vertex has three legs. A connected four-point <tree-level Feynman diagram> therefore needs two cubic vertices and one internal propagator. There are exactly three ways to partition the labeled external legs between these vertices:
``
s channel t channel u channel
p \ / p' p ---o--- p' p ---o--- q'
o--------o | |
q / \ q' q ---o--- q' q ---o--- p'
internal: p+q internal: p-p' internal: p-q'
``
Solid lines denote the <real scalar field> propagator. The labels specify which external pair meets at each vertex, so the last two graphs are different even though their unlabeled shapes agree. This is the <four-point tree amplitude in phi cubed theory>:
$$
\boxed{\text{three exchange diagrams, in the }s,t,u\text{ channels; each is of order }\lambda^2.}
$$
There is no four-point contact vertex in the given cubic interaction.
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