split into new gluons, and thus the proton structure is much more complicated. It was indeed observed in these collisions that almost half of the proton’s momentum is carried by particles that don’t interact electromagnetically, namely the gluons. Gluons and quarks are collectively called partons.

Let us consider a typical electron-proton scattering event, see figure 1. We have an incoming electron with four-momentum $p$ and an incoming proton with four-momentum $P$ interacting via the exchange of a virtual photon with virtuality $Q^{2}=-q^{2}$.

(250,150)(0,0) (0,0)(200,0) (0,5)(200,5) (0,10)(100,10) (100,10)(110,50) (0,100)(100,100) (100,100)(110,50)[4]{}[5]{} (100,100)(200,140) (110,50)(200,50) (50,90)\[\][$p$]{} (50,20)\[\][$P$]{} (115,30)\[\][$P'$]{} (115,80)\[\][$q$]{} (150,60)\[\][$P'+q$]{}

With $P'$ we denote the four-momentum of the parton which absorbs the virtual photon. The simplest possible process is that it stays on the mass-shell after the absorption, with a momentum $P'+q$. We define the variable $x$, as the fraction of the proton’s momentum carried by the parton, which is struck by the virtual photon; thus $ x=P'/P$. Since the mass of the proton, and naturally its partons, can be neglected at the energy scales we are concerned about, we get $ (P'+q)^{2}=0$ and $P'^{2}+2P'\cdot q+q^{2}=2xP\cdot q-Q^{2}=0$, and hence $x=\frac{Q^{2}}{2P\cdot
  q}$. This variable $x$ is called the Bjorken scaling variable, usually denoted by $x_{Bj}$.

