= Bound-state fusion of factorized S-matrices
{title2=$S_{C,D}(\vartheta)=S_{A,D}(\vartheta+iu/2)S_{A,D}(\vartheta-iu/2)$}
= Bound-state S-matrix fusion
{synonym}
For an equal-mass bound pair $C=(AA)$ at fusion <rapidity> $iu$, scatter a third particle off its two constituents with shifted <rapidities> and project onto the bound-state residue. Scalar amplitudes give the displayed product. With internal indices, bound-state coupling tensors perform the projection. The <Yang-Baxter equation> makes different scattering orders consistent; factorization eliminates independent many-body scattering contributions.
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