Partons quarks

Faced then with the need to introduce and discuss these more extensive calculations, and given that schoolchildren, so it seems, are taught about quarks and gluons, there was the temptation to abandon the long and leisurely historical introduction to partons, quarks and gluons that we had provided in the first edition. 

Since the discovery of the parton substructure of nucleons and its interpretation within the constituent quark model, much effort has been spent to explain the properties of these particles and the structure of high density phases of matter is under current experimental investigation in heavy-ion collisions [17]. While the diagnostics of a phase transition in experiments with heavy-ion beams faces the problems of strong non-equilibrium and finite size, the dense matter in a compact star forms a macroscopic system in thermal and chemical equilibrium for which effects signalling a phase transition shall be most pronounced [8],... 

The initial quark model was formulated to explain the diversity of the hadrons and not to explicitly describe the internal structure of any particle. It was inevitable, however, that with further research there w as a tendency to identify new findings with the hypothetical quarks. A number ofproperties of the partons, such as their intrinsic spin angular momentum, have been measured and have proved to be consistent with the predictions of the quark model. 

Close FE (1979) Introduction to quarks and partons, Academic, London... 

Close, F. E. An Introduction to Quarks and Partons. London, Academic Press 1979... 

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... 

In this chapter the theoretical concepts relevant to describe the physics of heavy quarks at the LHC are introduced. The main ideas of Quantum Chromodynamics are reviewed, before their appUcation to high-energy hadron-hadron collisions is discussed. This includes the factorization ansatz, the evolution of the parton distribution functions, the partonic processes important for beauty quark production and the phenomenological treatment of heavy quark fragmentation. A further section is dedicated to the description of the decay of -hadrons via the weak interaction. The Monte Carlo event generators which are used in this analysis to generate full hadronic events within the QCD framework are presented in the last section. 

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 short-distance, perturbative part Dq(x, fip) models the evolution of a quark produced off-shell at the scale /x/7 via gluon emissions to a quark on its mass shell. This is what is usually implemented in the parton shower algorithms of the Monte Carlo simulation programs. A parton shower develops through successive splitting until the perturbative approach becomes unreliable ( Aqcd)- The parton shower represents an approximative perturbative treatment of QCD dynamics based on the DGLAP evolution equations. It improves the fixed order pQCD calculation by taking into account soft and collinear enhanced terms to all orders. 

In case of cluster fragmentation models color-singlet clusters of partons form after the perturbative phase of jet development and then decay into the observed hadrons. The clusters originate from gluon splitting in quark pairs and subsequent recombination with neighboring quarks and antiquarks. Afterward, the clusters are assumed to decay isotropically in their rest frame into pairs of hadrons, where the branching ratios are determined by the density of states. 

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. 6.1. The approximate partial decay widths of H to all two-body partonic decay modes. The dashed curves show decays to charged leptons, the solid curves the decay into hadrons as computed from the contributions to each quark separately. The dot-dashed curves illustrate the two-gluon and two-photon decays. See text.

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. 

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 fundamental interaction is the electromagnetic scattering of the electron on a parton qi. The details of how the struck parton recombines with those partons that did not interact, so as to form physical hadrons, is not well understood. Since partons or quarks are assumed not to exist as real physical particles there must be unit probability for them to transmute into physical hadrons. 

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. 

It would be possible to argue from the above that the couphng to partons is not pure V—A. But a more natural approach, when we identify partons with quarks, is to insist on pure V — A coupling for quarks, but to allow the presence of quark-antiquark pairs in the hadrons. The antiquarks or antipartons, like antineutrinos, will couple through V A A and the deviation of rexp from will measure the proportion of antiquarks present in the hadron. 

Since the Cabibbo theory of weak interactions and its successor the SM gauge theory of weak and electromagnetic interactions are most simply formulated in terms of leptons and quarks, and since the low energy data are nicely consistent with this and a picture of the hadrons as built up from quarks, it would be most natural to expect that the point-like granules, the partons, discovered inside the hadrons, are in fact the quarks. Prom the point of view of hadron model building one tends to think of quarks as particles with a well-defined mass, whereas our partons have a continuous range of mass rrij = a mN(0 < a < 1). But, as mentioned earlier, the... 

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