When computing tree level scattering cross sections, if there is for example a $t$ and $u$ channel diagram, then the scattering amplitude will look like
$$\mathcal{M} = \mathcal{M}_t+\mathcal{M}_u.$$
When you take the magnitude, you get cross terms
$$|\mathcal{M}|^2 = |\mathcal{M}_t|^2+|\mathcal{M}_u|^2 + (\mathcal{M}_t\mathcal{M}_u^{\dagger}+\mathcal{M}_u\mathcal{M}_t^{\dagger}).$$
But these cross terms can be pesky and more often then not will vanish at the end of long calculations.
One thing that I had noticed is that if there is a sign difference between say $\mathcal{M}_t\mathcal{M}_u^{\dagger}$ and $\mathcal{M}_u\mathcal{M}_t^{\dagger}$, say due to some crossing symmetry, then the cross terms will not vanish. However, if there isn't a sign difference then the cross terms appear to vanish.
This may just be a coincidence, but I was wondering if there were some theorems which allows us to ignore the cross terms under certain conditions.
