= Longitudinal-vector annihilation through a scalar contact interaction
{title2=$\sigma_{LL}\sim g^4s/(32\pi m_A^4)$}
For a vertex $2ig^2\eta_{\mu\nu}$ and two identical outgoing real <scalar> <particles>, the longitudinal-pair amplitude is $g^2(s-2m_A^2)/m_A^2$. The high-energy <cross section> is the displayed expression, including the final-state factor $1/2!$. An <unpolarized cross section>[unpolarized] incoming pair averages over nine <spin> states and has leading <cross section> $g^4s/(288\pi m_A^4)$. A written interaction $g^2A_\mu A^\mu h^2$ instead gives vertex $4ig^2\eta_{\mu\nu}$ and four times these <cross sections>. The distinction separates a vertex normalization from <polarization> averaging and identical-particle phase-space counting.
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