Partons quark-parton model

QCD has the important property of asymptotic freedom - that at very high energies (and, hence, short distances) the interactions between quarks tend to zero as the distance between them tends to zero. Because of asymptotic freedom, perturbation theory maybe used to calculate the high energy aspects of strong interactions, such as those described by the parton modeL... 

Due to the asymptotic freedom in QCD, the interaction between quarks and gluons becomes arbitrarily weak at short distances. Consequently hadrons behave as collections of free partons at large transferred momenta and their interaction can therefore be described using a parton model. 

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. 

Estimates can be made, however, if we use the free quark-parton model and assume that partons convert into hadrons with unit probability. A very rough estimate for the inclusive semi-leptonic D decay can be obtained along the lines given previously [eqn (13.2.2)] if we forget all complications coming from non-spectator diagrams and assume that the light quark behaves purely like a spectator while the charm quark decay proceeds as if it were a free particle. In this case one has... 

We have seen in earlier chapters that there seems to be a close parallelism between the sets of leptons and the sets of quarks, at least in so far as the unified weak and electromagnetic interaction is concerned. The leptons are essentially point-like in their behaviour, and it is not inconceivable that the quarks too enjoy this property. In that case we might expect the hadrons to behave, in certain situations, in a less complicated fashion than usual. If we think of the hadrons as complicated atoms or molecules of quarks, then at high energies and momentum transfers, where we are probing the inner structure, we may discover a relatively simple situation, with the behaviour controlled by almost free, point-like constituents. The idea that hadrons possess a granular structure and that the granules behave as hard point-like, almost free (but nevertheless confined) objects, is the basis of Feynman s (1969) parton model. 

In order to understand the parton model properly one clearly requires a good understanding of the basic lepton-quark process... 

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. 

In the appendix to this chaper we shall develop a picture of the parton model as an impulse approximation in which better control of kinematic effects is possible. It turns out from eqn (16.9.36) that for CC reactions involving a transition from a light quark j to a heavy qumrk k the principal kinematic corrections are the following ... 

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°°. 

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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