Parton model

Asymptotic freedom explains the successes of the parton model of pointlike objects inside hadrons and enables systematic corrections to the parton model to be calculated using perturbation theory. That the in-... 

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. 

Fig. 33 Scattering process of two hadrons h and h2 in the parton model. Two partons with momentum fractions xi and X2 undeigo a hard interaction at the scale 2 ...

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... 

Fig. 5.4. Calculated parton model cross-sections for the production of W bosons in pp and pp collisions. Solid and dashed lines correspond to different assumed parton distribution functions. (Prom Quigg, 1977.)...

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 parton model, where the interaction is with point-like objects inside the hadron one finds an energy dependence analogous to that of purely leptonic scattering [see, for example, (5.1.27)]. 

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... 

Towards the parton model—deep inelastic scattering... 

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. 

The essence of the parton model is the assumption that, when a sufficiently high momentum transfer reaction takes place, the projectile, be it a lepton or a parton inside a hadron, sees the target as made up of almost free constituents, and is scattered by a single, free, effectively massless constituent. Moreover the scattering from individual constituents is incoherent. The picture thus looks much like the impulse approximation of nuclear physics. 

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

The above relations will be important in understanding the parton model for the structure functions Wj. 

If we were to assume SU(6) symmetry we would have Zp =, Zn = 0 which would imply Ai > 0 for protons at large Q, in contrast to (15.6.20). We shall see later that Ai > 0 also emerges from the parton model. 

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. 

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. 

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

Q /2mN ) plays a role. We have thus obtained the remarkable features of the deep inelastic structure functions mentioned earlier, and satisfied the Bjorken result (15.5.4). Indeed, in the above naive parton model we have... 

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