Phi cubed theory (${\varphi }^3$ theory)

Phi cubed theory has interaction $-g{\varphi }^3/3!$, giving a cubic vertex $-ig$. In four spacetime dimensions the scalar field has mass dimension one and $g$ has mass dimension one.

A connected five-point tree in phi cubed theory has three cubic vertices and two internal propagators. For labeled external legs there are fifteen diagrams: choose the leg attached to the middle vertex and partition the other four legs into two unordered pairs.