## Deep inelastic scattering processes and the parton model for hadrons

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One of the greatest puzzles of elementary particle physics is the structure of the hadrons. Recent experiments at SLAC have found unexpectedly large cross-sections for large momentum transfers from the electron in high-energy electron-proton scattering, and this has led to the suggestion(l) that these experiments are discovering the existence of point electromagnetic charges within the proton. The supposed carriers of these point charges hav~_ been called partons. The cross-section measured in these experiments is that corresponding to the diagram of fig. 1, under the assumption that only the lO1-J'est order e,. ' >e p ~ ~H Fig. 1 term in the expansion in p0i-TerS of the fine structure constant is significant. In the laboratory system an electron of energy E is scattered off a proton at rest, emerging at a scattering angle & .nth energy E:/, and only these parameters of the scattered electron are measured, the final states H of the hadronic system being ignored. The hadronic process is then parametrised by the Lorentz invariants and y ",I: (1.1) (1.2) 2. The experiments can be regarded as measuring the total cross-section for scattering virtual photons on protons. This is described by a squared matrix element summed over all hadronic states consistent with appropriate conservation laws ~ < r-/JfA ( 0) I H(r1) < H(fJ/J'){o)0) x. (277)1,. J(+J(r<-r-'t) which can be written as ·thematrix element of a current commutator Using current conservation we can write . . • Wr '(f;1J:: (-/' + 'k;{) \IV;' ~)J) . .

- (f - { ? ) ( ; - ~ 7' ) t1( ~ V), The ~caling hypothesis(2) states that, in the limit (1.3) -v -7 c-o (1.6) r. \ == 2-Y fixed, vv -7 called the Bjorken limit, the structure functions have scaling behaviour w (~~))) ~f;(w) )l VV2- (CY~Y) ~F; (w). (1.8) In other words it is suggested that, at large V and CV~ , W, and y vK should become functions only of the dimensionless quantity W •