Cross section from the scattering amplitude with derivative

Suppose we have a process with two particles in and two particles out. The amplitude for such process is given by

$$ M_0 (2pi)^4 delta(p’+l_2-l_1-p)+M_1 (2pi)^4 delta_{1,2,-}(p’+l_2-l_1-p)delta_+'(p’+l_2-l_1-p)$$

where $x^{pm} = x^0 pm x^3$ are lightfront coordinates. $M_0$ is the leading contribution, and $M_1$ is a correction to the amplitude. Unlike the first term, the correction has the derivative of a delta function.

How can one compute the cross section from this?