Unpolarized cross section ($\overline{|\mathcal{M}{|}^2}=\frac{1}{(2s_1+1)(2s_2+1)}{\sum }_{\mathrm{initial},\mathrm{final}}|\mathcal{M}{|}^2$)

For uncorrelated incoming beams with equally populated spin states, the measured cross section averages over initial polarizations and sums over unobserved final polarizations. The displayed average applies to two massive incoming particles with spins $s_1,s_2$. It is distinct from a prepared-polarization channel and from the final-state identical-particle factor in a final-state phase-space integral. A polarization channel with an amplitude that grows faster than the others can reach a perturbative bound before the averaged quantity does.