Scattering Amplitudes for Phi 4 Theory

[Diracobama2181]

TL;DR Summary

How do if calculate ##i\mathcal{M}(\vec{ k_1}\vec{ k_2}\rightarrow \vec{ p_1}\vec{ p_2})(2\pi)^4\delta^{ (4)}(p_1 +p_2-k_1-k_2)## to 1 loop order?

I know $$ i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2) $$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element $$\bra{\vec{p_2}\vec{p_1}}\hat{S}\ket{\vec{k_1}\vec{k_2}}$$, would 1 loop just be the first order expansion ($$\frac{\lambda}{4!}\int d^4z\bra{\vec{p_1}\vec{p_2}}\phi\phi\phi\phi\ket{\vec{k_1}\vec{k_2}}$$) in this case?

 

[Diracobama2181]

Never mind. Figured it out. I would have to go to $$\lambda^2$$ in the expansion. Thanks.