Inelasticity ($y=P\cdot q/(P\cdot p)$)

The inelasticity in deep inelastic scattering is $y=P\cdot q/(P\cdot p)$, where $p$ is the incoming lepton momentum, $P$ the target momentum and $q$ the transfer. In the target rest frame it is the fraction of the incoming lepton energy transferred to the target. It is unchanged by replacing $P$ by a collinear parton momentum $\xi P$, and $Q^2=xyS$ in massless kinematics.