Proton structure, Partons, QCD, DGLAP and beyond

We present an introductory discussion of deep-inelastic lepton-proton scattering as a means to probe the substructure of the proton. A résumé of QCD is given, emphasizing the running of the coupling constant and the DGLAP evolution equations for the parton densities. The determination of parton distributions is discussed and their importance for predictions of processes at the LHC is emphasized. Going beyond the pure DGLAP regime, we briefly discuss the behaviour of parton densities at low x, and the evidence for non-linear absorptive contributions. 1 Deep inelastic scattering (DIS) introduced High energy electron scattering is an ideal probe of the structure of a composite object. For instance, consider the scattering of a beam of electrons on a nuclear target of mass MN . The scattering occurs via the exchange of a virtual photon, see Fig. 1. Since it is virtual, the photon is not on its mass shell. That is, its 4-momentum q does not satisfy q = 0. On the other hand, a real (ingoing or outgoing) particle or system must be on its mass shell. So the invariant mass W of the outgoing system in Fig. 1 satisfies W 2 = (pN + q) 2 = M N + 2pN · q + q, (1) Figure 1: Electron-nucleus scattering, where pN and q are the 4-momenta of the incoming nucleus and virtual photon respectively, and W is the invariant mass of the outgoing hadronic system. The lower three diagrams are a schematic illustration of the cross section for electronnucleus scattering, eN → eX, plotted as a function of the scaling variable xN = Q/2pN · q at three different values of Q. In the lowest plot the wavelength λ of the virtual photon probe is much less that the nuclear radius RN , and the photon probes a constituent proton of the nucleus.