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The $t$-channel singularity of a cross-section for a binary $2 \to 2$ scattering process occurs when a particle exchanged in the $t$ channel is kinematically allowed to be on its mass-shell, that is when the process can be viewed as a sequence of two physical subprocesses: a two-body decay $1\to 2$ and an inverse decay $2 \to 1$.
doi:10.1007/BF01366453
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