Tree-level Feynman diagram

A tree-level diagram has no loops and gives the leading classical contribution allowed by the interaction vertices.

For three real scalar fields with field interaction term ${\mathcal{L}}_I=-\frac{1}{2}(g_1{\varphi }^2\Phi +g_2{\psi }^2\Phi )$ and mediator mass $M$, the connected tree-level Feynman diagram for $\varphi \psi \to \varphi \psi$ has one exchanged $\Phi$ and Mandelstam invariant $t=(p-p^{\prime }{)}^2$. Each vertex has a factor $-i{g}_j$: its two identical-field Wick contractions cancel the factor $1/2$. Thus $i\mathcal{M}=(-i{g}_1)(-i{g}_2)i/(t-M^2+i0)$. There is no $s$- or $u$-channel at this order because the interaction has no mixed $\varphi \psi \Phi$ vertex. Distinguishable external particles also require no exchange symmetrization.