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I think I actually have an answer to this question even though I put a bounty on it. The idea is that the amplitude is maximal when the $W$ bosons are produced on-shell (since the propagators are the largest in this limit). This allows us to treat the creation of the $ W $'s separately from the rest of the diagram. The momenta of the particles in the lab ...


Short answer: you don't. Slightly longer answer: You're using beams of particles, and you focus each of them as much as you (practically1) can so that the particles in each beam are reasonably close together. The result is a wide variety of interaction distances from far apart through near misses to closer interactions still. You mentioned electrons ...

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