Use the Minkowski metric and choose the incoming electron along , with the scattered electron in the plane. In natural units, neglecting the electron mass, the four-momenta are
(1)
The momentum transfer entering the proton is therefore
(2)
The outgoing hadronic system carries . The energy transfer is , while need not point along the original beam.
Figure 1.
Fixed-target deep inelastic scattering: laboratory directions and a schematic detector
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