14
QCD I: Introduction, Tree Graph
Predictions, and Jets
In the previous chapter we have introduced the elementary concepts and formalism associated with non-Abelian quantum gauge field theories. It is now
well established that the strong interactions between quarks are described by
a theory of this type, in which the gauge group is an SU(3) c , acting on a
degree of freedom called ‘colour’ (indicated by the subscript c). This theory
is called Quantum Chromodynamics, or QCD for short. QCD will be our first
application of the theory developed in chapter 13, and we shall devote the
next two chapters, and much of chapter 16, to it.
In the present chapter we introduce QCD and discuss some of its simpler
experimental consequences. We briefly recall the evidence for the ‘colour’ degree of freedom in section 14.1, and then proceed to the dynamics of colour,
and the QCD Lagrangian, in section 14.2. Perhaps the most remarkable thing
about the dynamics of QCD is that, despite its being a theory of the strong
interactions, there are certain kinematic regimes – roughly speaking, short distances or high energies – in which it is effectively a quite weakly interacting theory. This is a consequence of a fundamental property, possessed only by nonAbelian gauge theories, whereby the effective interaction strength becomes
progressively smaller in such regimes. This property is called ‘asymptotic
freedom’, and was already mentioned in section 11.5.3 of volume 1. In appropriate cases, therefore, the lowest-order perturbation theory amplitudes (tree
graphs) provide a very convincing qualitative, or even ‘semi-quantitative’, orientation to the data. In sections 14.3 and 14.4 we shall see how the tree graph
techniques acquired for QED in volume 1 produce more useful physics when
applied to QCD.
However, most of the quantitative experimental support for QCD has come
from comparison with predictions which include higher-order QCD corrections; indeed, the asymptotic freedom property itself emerges from summing a
whole class of higher-order contributions, as we shall indicate at the beginning
of chapter 15. This immediately involves all the apparatus of renormalization.
The necessary calculations quite rapidly become too technical for the intended
scope of this book, but in chapter 15 we shall try to provide an elementary introduction to the issues involved, and to the necessary techniques, by building
on the discussion of renormalization given in chapters 10 and 11 of volume 1.
The main new concept will be the renormalization group (and related ideas),
73
QCD I: Introduction, Tree Graph
Predictions, and Jets
In the previous chapter we have introduced the elementary concepts and formalism associated with non-Abelian quantum gauge field theories. It is now
well established that the strong interactions between quarks are described by
a theory of this type, in which the gauge group is an SU(3) c , acting on a
degree of freedom called ‘colour’ (indicated by the subscript c). This theory
is called Quantum Chromodynamics, or QCD for short. QCD will be our first
application of the theory developed in chapter 13, and we shall devote the
next two chapters, and much of chapter 16, to it.
In the present chapter we introduce QCD and discuss some of its simpler
experimental consequences. We briefly recall the evidence for the ‘colour’ degree of freedom in section 14.1, and then proceed to the dynamics of colour,
and the QCD Lagrangian, in section 14.2. Perhaps the most remarkable thing
about the dynamics of QCD is that, despite its being a theory of the strong
interactions, there are certain kinematic regimes – roughly speaking, short distances or high energies – in which it is effectively a quite weakly interacting theory. This is a consequence of a fundamental property, possessed only by nonAbelian gauge theories, whereby the effective interaction strength becomes
progressively smaller in such regimes. This property is called ‘asymptotic
freedom’, and was already mentioned in section 11.5.3 of volume 1. In appropriate cases, therefore, the lowest-order perturbation theory amplitudes (tree
graphs) provide a very convincing qualitative, or even ‘semi-quantitative’, orientation to the data. In sections 14.3 and 14.4 we shall see how the tree graph
techniques acquired for QED in volume 1 produce more useful physics when
applied to QCD.
However, most of the quantitative experimental support for QCD has come
from comparison with predictions which include higher-order QCD corrections; indeed, the asymptotic freedom property itself emerges from summing a
whole class of higher-order contributions, as we shall indicate at the beginning
of chapter 15. This immediately involves all the apparatus of renormalization.
The necessary calculations quite rapidly become too technical for the intended
scope of this book, but in chapter 15 we shall try to provide an elementary introduction to the issues involved, and to the necessary techniques, by building
on the discussion of renormalization given in chapters 10 and 11 of volume 1.
The main new concept will be the renormalization group (and related ideas),
73