9
Deep Inelastic Electron–Nucleon Scattering
and the Parton Model
We have obtained the rules for doing calculations of simple processes in quantum electrodynamics for particles of spin-0 and spin1 , and many explicit
2
examples have been considered. In this chapter we build on these results to
give an (admittedly brief) introduction to a topic of central importance in particle physics, the structure of hadrons as revealed by deep inelastic scattering
experiments (the equally important neutrino scattering experiments will be
discussed in volume 2). We do this partly because the necessary calculations
involve straightforward, illustrative and eminently practical applications of
the rules already obtained, but, more particularly, because it is from a comparison of these calculations with experiment that compelling evidence was
obtained for the existence of the point-like constituents of hadrons – quarks
and gluons – the interactions of which are described by QCD.
9.1 Inelastic electron–proton scattering: kinematics and
structure functions
At large momentum transfers there is very little elastic scattering: inelastic
scattering, in which there is more than just the electron and proton in the final
state, is much more probable. The simplest inelastic cross section to measure
is the so-called ‘inclusive’ cross section, for which only the final electron is
observed. This is therefore a sum over the cross sections for all the possible
hadronic final states: no attempt is made to select any particular state from
the hadronic debris created at the proton vertex. This process may be represented by the diagram of figure 9.1, assuming that the one-photon exchange
amplitude dominates. The ‘blob’ at the proton vertex indicates our ignorance
of the detailed structure: X indicates a sum over all possible hadronic final
states. However, the assumption of one-photon exchange, which is known
experimentally to be a very good approximation, means that, as in our previous examples (cf (8.118) and (8.185)), the cross section must factorize into
a leptonic tensor contracted with a tensor describing the hadron vertex:
dσ ∼ L μν W
μν (q, p).
(9.1)
269
Deep Inelastic Electron–Nucleon Scattering
and the Parton Model
We have obtained the rules for doing calculations of simple processes in quantum electrodynamics for particles of spin-0 and spin1 , and many explicit
2
examples have been considered. In this chapter we build on these results to
give an (admittedly brief) introduction to a topic of central importance in particle physics, the structure of hadrons as revealed by deep inelastic scattering
experiments (the equally important neutrino scattering experiments will be
discussed in volume 2). We do this partly because the necessary calculations
involve straightforward, illustrative and eminently practical applications of
the rules already obtained, but, more particularly, because it is from a comparison of these calculations with experiment that compelling evidence was
obtained for the existence of the point-like constituents of hadrons – quarks
and gluons – the interactions of which are described by QCD.
9.1 Inelastic electron–proton scattering: kinematics and
structure functions
At large momentum transfers there is very little elastic scattering: inelastic
scattering, in which there is more than just the electron and proton in the final
state, is much more probable. The simplest inelastic cross section to measure
is the so-called ‘inclusive’ cross section, for which only the final electron is
observed. This is therefore a sum over the cross sections for all the possible
hadronic final states: no attempt is made to select any particular state from
the hadronic debris created at the proton vertex. This process may be represented by the diagram of figure 9.1, assuming that the one-photon exchange
amplitude dominates. The ‘blob’ at the proton vertex indicates our ignorance
of the detailed structure: X indicates a sum over all possible hadronic final
states. However, the assumption of one-photon exchange, which is known
experimentally to be a very good approximation, means that, as in our previous examples (cf (8.118) and (8.185)), the cross section must factorize into
a leptonic tensor contracted with a tensor describing the hadron vertex:
dσ ∼ L μν W
μν (q, p).
(9.1)
269