= Elastic scattering from a quartic scalar contact interaction
{title2=$d\sigma_{\rm event}/d\Omega=\lambda^2/(128\pi^2s)$}
The factorial-normalized quartic vertex gives an angle-independent tree amplitude of magnitude $|\lambda|$. For equal incoming and outgoing masses, the momentum ratio in the two-body cross-section cancels. The event density for identical outgoing particles over a full sphere is $\lambda^2/(128\pi^2s)$. On a hemisphere representing each event once, the density is $\lambda^2/(64\pi^2s)$. Both conventions give total event cross-section $\lambda^2/(32\pi s)$.
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