6. Structure Functions 16.1. Deep Inelastic Scattering

ν = q · P M = E − E′ is the lepton’s energy loss in the nucleon rest frame (in earlier literature sometimes ν = q · P ). Here, E and E′ are the initial and final lepton energies in the nucleon rest frame. Q2 = −q2 = 2(EE′−−→k · −→k ′)−m2 −m2 ′ where m (m ′) is the initial (final) lepton mass. If EE′ sin2(θ/2) m2 , m2 ′ , then ≈ 4EE′ sin2(θ/2), where θ is the lepton’s scattering angle with respect to the lepton beam direction. x = Q2 2Mν where, in the parton model, x is the fraction of the nucleon’s momentum carried by the struck quark.