The detailed quark-parton model

For each type (flavour) of quark-parton or antiquark-antiparton we now allow a separate distribution function u(a ), d(x), s x) and u(a ), d x),s x) giving the nmnber densities of such objects with momentum fraction be- 

Note that we do not consider any fundamental component of c, b or t quarks in the nucleon. Their presence, in the form of qq pairs, is better thought of as a dynamic effect arising from pair production from gluons (see Fig. 16.10), i.e. a QCD effect, and will be treated in Section 23.8. This means that the formulae for the scaling functions to be presented in this section require additional contributions to be added to them when the kinematics is such as to allow charm or bottom production. Given present estimates of the top mass the production of top is not a relevant consideration. 

Because of the existence of the sea, whose excitation seems to depend upon u, we should not expect the RHS of (16.4.1) to be a constant, nor indeed to be particularly meaningful. On the other hand, if we ask for the net number of say u quarks in the proton we must find 2. Thus 

A more rigorous derivation of these results is given in Section 16.9.3 in the appendix to this chapter. The above equations, which simply express the overall quark content of a proton, will be the basis for various sum rules that can be tested experimentally. Notice that they do not imply s(x) = s(x), though this seems very reasonable and is often assumed in the following. 

Because, by definition, the valence quarks give the proton its correct 517(2) or 517(3) properties, we e jq ect the sea to be basically neutral, i.e. singlet under these transformations. But the above symmetries are not perfect, and while 517(2) is well respected, in nature 517(3) is broken somewhat. It thus seems reasonable, for the proton, to insist in the simple picture that 

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There is an elaborate and beautiful picture built upon this idea, the quark-parton model, which we shall investigate in detail in Chapters 15-17. In the framework of this model very precise and detailed tests of the standard model can be made, and we shall be content, at this point, to note that all aspects of the SM theory are consistent with experiments of the inclusive type up to the present. 

Let us now turn to NC reactions. In Section 10.1 we discussed certain NC results which did not depend upon our detailed picture of hadrons. We now look at more specific predictions that follow in the quark-parton model. Thus substituting (16.4.41-43) into (15.5.9) yields... 

We shall discuss the model in some detail in the following chapters, in particular the question as to whether the partons can be identified with the quarks. The introductory material of the chapter is largely based upon lecture notes of F. Close (1973) (see also Close, 1979). We shall also study more sophisticated versions of the picture, wherein the quark-partons are not treated as free, but are allowed to interact with each other via the exchange of gluons, in the framework of QCD. 

The quark-paxton model was developed in great detail in the previous chapter. Here we discuss the experimental situation and confront the theory with the vast amoimt of data on deep inelastic scattering and related reactions. It must be borne in mind that we have not yet discussed the QCD corrections to the model. These are not small, but their dominant effect can be taken into account by allowing the parton number densities to depend upon in a way calculable in QCD, so that, fortuitously, the entire formalism is basically unchanged, except that each qj x) —> qj x,Q ). As mentioned earlier this implies a dynamical breaking of perfect Bjorken scaling. It also implies that if one is seeking accurate information about the qj x) from experiment then care must be taken to specify the involved. 

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