Two-body scattering cross section ($\frac{d\sigma }{d\Omega }=\frac{1}{64{\pi }^{2}s}\frac{|{\mathbf{k}}_f|}{|{\mathbf{p}}_i|}\overline{|\mathcal{M}{|}^2}$)

For distinguishable final particles, the centre-of-momentum frame cross section is the displayed product of the invariant amplitude, incoming flux and relativistic two-body phase space. Initial unpolarized states are averaged; unobserved final polarizations are summed. An isotropic amplitude integrates to $\sigma =(|{\mathbf{k}}_f|/|{\mathbf{p}}_i|)\overline{|\mathcal{M}{|}^2}/(16\pi s)$. A full-solid-angle integral for identical final particles additionally needs its symmetry factor.