The quark-parton model

Finally we warn the reader that to meet the phenomenal accuracy of recent experiments it is necessary to give careful attention to kinematic details which to some extent detract from the elegant simplicity of the original picture. These effects are treated in the appendix to this chapter (Section 16.9) in which the parton model is reformulated as an impulse approximation which allows better control of the kinematic factors. The chapter can be perfectly well understood without reading the appendix. 

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The main production mechanism and its subsequent decay say into can be visualized in the quark-parton model as in Fig. 5.3. Let /s be the CM energy of the pp collision. The cross-section s) to produce a of invariant mass /s will depend upon the elementary cross-section for ud —> multiplied by the flux of u and d... 

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. 

In the following chapter we shall see how the quark-parton model explains the occurrence of Bjorken scaling and we shall obtain expressions for all the scaling functions in terms of number densities for the quark-partons in a hadron. 

We begin with a qualitative discussion of the quark-parton model. A more careful and quantitive description is gradually developed thereafter. 

Taken seriously the quark-parton model is exciting because it offers a host of testable relations to which we now turn. 

This completes the specification of the quark-parton model formulae for the scaling functions relevant to scattering on an unpolarized nucleon target in the region [Pg.374]

First we note that in the quark-parton model we have, as can be seen from Table 9.1,... 

Let us now consider what can be learnt about the parton structure from polarized deep inelastic experiments. In the quark-parton model (16.8.11) becomes... 

Current matrix elements in the quark-parton model... 

In the SM all hadronic currents are expressed in terms of quark fields f x) where / labels the fiavour. As in Sections 1.2, 16.8 and 18.1, we often require the forward matrix elements of these currents taken between nucleon states. We shall use the quark-parton model to evaluate these in the firame S°°. 

Let us now look at some of the relations amongst the scaling functions in the quark-parton model. We shall see that where these have been tested the results are, with one exception at present, generally in agreement with the predictions. 

Then using the quark-parton model expression (16.8.21) for 5i(x), (17.1.18) implies... 

Neutrino cross-sections in the quark—parton model for... 

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... 

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