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Some issues of recoil effects in AdS/CFT are studied from the point of viewof OPE expansions for generalized free fields. We show that the conformal groupstructure encodes the relative energies and momenta at a collision center. Thisis done by being careful with the analysis of Clebsch-Gordan coefficients foran $SL(2)$ subalgebra of the conformal group. The collision fraction of kineticenergy carried by the particles is derived from a probability distribution thatarises from these coefficients. We specifically identify a precise statement ofwhen recoil of a heavy particle in AdS can be ignored: the maximum probabilityis for the heavy particle to be in its ground state. We also argue how a notionof reduced mass appears in these collisions, in the limit where the particlesare moving slowly with respect to each other. This controls the notion of theimpact parameter of the collision.

Operator product expansions and recoil