86
14. QCD I: Introduction, Tree Graph Predictions, and Jets
where M n is the neutron mass. This would imply θ < 10
−12 . In fact, this
estimate is too restrictive, since it turns out (Weinberg 1996, section 23.6)
that if any quark has zero mass, θ can be reduced to zero by a global chiral
U(1) transformation on that quark field. Although neither of the u and d
quark masses are zero, they are small on a hadronic scale, and a suppression
of (14.45) is expected, increasing the bound on theta. Estimates suggest
θ < 10
−9
− 10
−10 .
This may seem an unsatisfactorily special value to force on a dimensionless
Lagrangian parameter, when there is nothing in the theory, a priori, to prevent
something of order unity. This perceived difficulty is referred to as the ‘strong
CP problem’. A possible solution to the problem, in which a very small value
of θ could arise naturally was suggested by Peccei and Quinn (1977a, 1977b).
Their idea goes beyond the Standard Model, and involves the existence of a
new very light pseudoscalar particle, the axion (Wilczek 1978, Winberg 1978).
We proceed now with the main topic of this chapter, which is the application of perturbative QCD.
14.3 Hard scattering processes, QCD tree graphs, and
jets
14.3.1 Introduction
The fundamental distinctive feature of non-Abelian gauge theories is that they
are ‘asymptotically free’, meaning that the effective coupling strength becomes
progressively smaller at short distances, or high energies (Gross and Wilczek
1973, Politzer 1973). This property is the most compelling theoretical motivation for choosing a non-Abelian gauge theory for the strong interactions, and
it enables a quantitative perturbative approach to be followed (in appropriate
circumstances) even in strong interaction physics. This programme has indeed been phenomenally successful, firmly establishing QCD as the theory of
strong interactions, and now – in the era of the LHC – serving as a precision
tool to guide searches for new physics.
A proper understanding of how this works necessitates a considerable detour, however, into the physics of renormalization. In particular, we need to
understand the important cluster of ideas going under the general heading of
the ‘renormalization group’, and this will be the topic of chapter 15. For the
moment we proceed with a discussion of some simple tree-level applications
of QCD, which provided early confrontation of QCD with experiment.
Let us begin by recapitulating, from a QCD-informed viewpoint, how
2
the parton model successfully interpreted deep inelastic and large-Q data
in terms of almost free point-like partons – now to be identified with the QCD
quanta: quarks, antiquarks, and gluons.
14. QCD I: Introduction, Tree Graph Predictions, and Jets
where M n is the neutron mass. This would imply θ < 10
−12 . In fact, this
estimate is too restrictive, since it turns out (Weinberg 1996, section 23.6)
that if any quark has zero mass, θ can be reduced to zero by a global chiral
U(1) transformation on that quark field. Although neither of the u and d
quark masses are zero, they are small on a hadronic scale, and a suppression
of (14.45) is expected, increasing the bound on theta. Estimates suggest
θ < 10
−9
− 10
−10 .
This may seem an unsatisfactorily special value to force on a dimensionless
Lagrangian parameter, when there is nothing in the theory, a priori, to prevent
something of order unity. This perceived difficulty is referred to as the ‘strong
CP problem’. A possible solution to the problem, in which a very small value
of θ could arise naturally was suggested by Peccei and Quinn (1977a, 1977b).
Their idea goes beyond the Standard Model, and involves the existence of a
new very light pseudoscalar particle, the axion (Wilczek 1978, Winberg 1978).
We proceed now with the main topic of this chapter, which is the application of perturbative QCD.
14.3 Hard scattering processes, QCD tree graphs, and
jets
14.3.1 Introduction
The fundamental distinctive feature of non-Abelian gauge theories is that they
are ‘asymptotically free’, meaning that the effective coupling strength becomes
progressively smaller at short distances, or high energies (Gross and Wilczek
1973, Politzer 1973). This property is the most compelling theoretical motivation for choosing a non-Abelian gauge theory for the strong interactions, and
it enables a quantitative perturbative approach to be followed (in appropriate
circumstances) even in strong interaction physics. This programme has indeed been phenomenally successful, firmly establishing QCD as the theory of
strong interactions, and now – in the era of the LHC – serving as a precision
tool to guide searches for new physics.
A proper understanding of how this works necessitates a considerable detour, however, into the physics of renormalization. In particular, we need to
understand the important cluster of ideas going under the general heading of
the ‘renormalization group’, and this will be the topic of chapter 15. For the
moment we proceed with a discussion of some simple tree-level applications
of QCD, which provided early confrontation of QCD with experiment.
Let us begin by recapitulating, from a QCD-informed viewpoint, how
2
the parton model successfully interpreted deep inelastic and large-Q data
in terms of almost free point-like partons – now to be identified with the QCD
quanta: quarks, antiquarks, and gluons.