5 QCD on the Lattice
139
with the use of alternative discretizations that are numerically more efficient. At
the time of writing this contribution (2007), the whole field is actually in a state
of transition: although the quenched approximation is being abandoned, the latest
results from simulations with dynamical quarks have not yet reached the same level
of accuracy in regard to controlling systematic errors due to lattice artefacts and
effects from renormalization, as compared to earlier quenched calculations. It can
thus be expected that many of the results discussed later in this chapter will soon
be superseded by more accurate numbers. In turn, the quenched approximation will
be completely obsolete in a few years time, except perhaps to test new ideas or for
exploratory studies of more complex quantities.
5.1.2 Outline
We begin with an introduction of the basic concepts of the lattice formulation of
QCD. This shall include the field theoretical foundations, discretizations of the QCD
Lagrangian, as well as simulation algorithms and other technical aspects related to
the actual calculation of physical observables from suitable correlation functions.
The following sections deal with various applications. Lattice calculations of
the hadron spectrum are described in Sect. 5.3. Section 5.4 is devoted to lattice
investigations of the confinement phenomenon. Determinations of the fundamental
parameters of QCD, namely the strong coupling constant and quark masses are
a major focus of this article, and are presented in Sect. 5.5. Another important
property of QCD, namely the spontaneously broken chiral symmetry, is discussed in
some detail in Sect. 5.6, which also includes a brief introduction into analytical nonperturbative approaches to the strong interaction, based on effective field theories.
Lattice calculations of weak hadronic matrix elements, which serve to pin down the
elements of the Cabibbo–Kobayashi–Maskawa matrix, are covered in Sect. 5.7. We
end this contribution with a few concluding remarks.
In addition to the topics listed above, lattice simulations of QCD have also
made important contributions to the determination of the phase structure of QCD,
including results for the critical temperature of the deconfinement phase transition.
Nevertheless, in this chapter we restrict the discussion to QCD at zero temperature
and refer the reader to other parts of this volume.
5.2 The Lattice Approach to QCD
The essential features of the lattice formulation can be summarized by the following
statement:
Lattice QCD is the non-perturbative approach to the gauge theory of the strong interaction
through regularized, Euclidean functional integrals. The regularization is based on a
discretization of the QCD action which preserves gauge invariance at all stages.
139
with the use of alternative discretizations that are numerically more efficient. At
the time of writing this contribution (2007), the whole field is actually in a state
of transition: although the quenched approximation is being abandoned, the latest
results from simulations with dynamical quarks have not yet reached the same level
of accuracy in regard to controlling systematic errors due to lattice artefacts and
effects from renormalization, as compared to earlier quenched calculations. It can
thus be expected that many of the results discussed later in this chapter will soon
be superseded by more accurate numbers. In turn, the quenched approximation will
be completely obsolete in a few years time, except perhaps to test new ideas or for
exploratory studies of more complex quantities.
5.1.2 Outline
We begin with an introduction of the basic concepts of the lattice formulation of
QCD. This shall include the field theoretical foundations, discretizations of the QCD
Lagrangian, as well as simulation algorithms and other technical aspects related to
the actual calculation of physical observables from suitable correlation functions.
The following sections deal with various applications. Lattice calculations of
the hadron spectrum are described in Sect. 5.3. Section 5.4 is devoted to lattice
investigations of the confinement phenomenon. Determinations of the fundamental
parameters of QCD, namely the strong coupling constant and quark masses are
a major focus of this article, and are presented in Sect. 5.5. Another important
property of QCD, namely the spontaneously broken chiral symmetry, is discussed in
some detail in Sect. 5.6, which also includes a brief introduction into analytical nonperturbative approaches to the strong interaction, based on effective field theories.
Lattice calculations of weak hadronic matrix elements, which serve to pin down the
elements of the Cabibbo–Kobayashi–Maskawa matrix, are covered in Sect. 5.7. We
end this contribution with a few concluding remarks.
In addition to the topics listed above, lattice simulations of QCD have also
made important contributions to the determination of the phase structure of QCD,
including results for the critical temperature of the deconfinement phase transition.
Nevertheless, in this chapter we restrict the discussion to QCD at zero temperature
and refer the reader to other parts of this volume.
5.2 The Lattice Approach to QCD
The essential features of the lattice formulation can be summarized by the following
statement:
Lattice QCD is the non-perturbative approach to the gauge theory of the strong interaction
through regularized, Euclidean functional integrals. The regularization is based on a
discretization of the QCD action which preserves gauge invariance at all stages.