Previously I asked the question Mandelstam variables high-energy limit in which it was said that the result $stu \approx -s^2 t$ for $s$ large was derived in the forward limit ($t \rightarrow 0$) and $s \rightarrow \infty$ (and $u/s \rightarrow -1$). I have some vertex which I want to simplify in the large $s$ limit:
\begin{equation} -\frac{9}{4} c^2 s(u+t)^2, \end{equation}
where $c$ is some coupling constant. I want to show that this becomes something like $-c_1 s^2 t +c_2 m^2 s^2$ for $s$ large for some constants $c_1,c_2$. But with the previously posted answer in Mandelstam variables high-energy limit I couldn't succeed. I was thinking about using the formula $4m^2 = u+t+s$ but I don't see how I can get rid of the $s^3$ term when $m^2$ gets introduced.
Does someone have an idea how this limit can be recovered?
