232
H. Wittig
where the first error is statistical, while the second represents an estimate of various
systematic uncertainties added in quadrature. Again, this result can be combined
with the experimental decay rate to determine |V cb |. More details can be found in
[240].
Most lattice studies of heavy-to-heavy semi-leptonic B-decays have been
restricted to the quenched approximation. However, results for the form factors
from dynamical simulations can be expected in the near future. Clearly, in order
to have maximum impact on the determination of |V cb |, systematic effects arising
from lattice artefacts and the formulation used to treat the heavy quark must be
controlled to a high degree.
5.8 Concluding Remarks
In this article we have introduced the lattice approach to QCD and discussed
a variety of applications, which range from hadron spectroscopy, confinement,
quark masses and the running coupling, to spontaneous chiral symmetry breaking
and hadronic matrix elements for flavour physics. This illustrates not only the
versatility of the lattice method, but also indicates that lattice calculations have
become ever more important for making quantitative predictions in the notoriously
difficult sector of non-perturbative QCD. Still, a great number of other applications
have not even been covered here, including nucleon structure functions and form
factors, calculations at finite temperature and/or chemical potential, or detailed
investigations of the QCD vacuum structure.
That lattice calculations have reached this standing is owed to the enormous
progress which been made in developing more efficient algorithms for dynamical
fermions, better discretizations, as well as a number of new theoretical concepts
such as non-perturbative renormalization. These developments, in conjunction
with the availability of ever more powerful computers, shall allow for precise
computations of many phenomenologically relevant quantities, which previously
seemed virtually intractable.
5.9 Addendum: QCD on the Lattice
5.9.1 Introduction
Since the first edition of this article [241] the field of lattice QCD has undergone
a huge transformation. While the actual methodology was well established at
the time of writing (2007), few simulations employing dynamical quarks had
produced results with controlled errors, having a direct impact on phenomenology
and experiment. During the past ten years or so this has changed dramatically.
H. Wittig
where the first error is statistical, while the second represents an estimate of various
systematic uncertainties added in quadrature. Again, this result can be combined
with the experimental decay rate to determine |V cb |. More details can be found in
[240].
Most lattice studies of heavy-to-heavy semi-leptonic B-decays have been
restricted to the quenched approximation. However, results for the form factors
from dynamical simulations can be expected in the near future. Clearly, in order
to have maximum impact on the determination of |V cb |, systematic effects arising
from lattice artefacts and the formulation used to treat the heavy quark must be
controlled to a high degree.
5.8 Concluding Remarks
In this article we have introduced the lattice approach to QCD and discussed
a variety of applications, which range from hadron spectroscopy, confinement,
quark masses and the running coupling, to spontaneous chiral symmetry breaking
and hadronic matrix elements for flavour physics. This illustrates not only the
versatility of the lattice method, but also indicates that lattice calculations have
become ever more important for making quantitative predictions in the notoriously
difficult sector of non-perturbative QCD. Still, a great number of other applications
have not even been covered here, including nucleon structure functions and form
factors, calculations at finite temperature and/or chemical potential, or detailed
investigations of the QCD vacuum structure.
That lattice calculations have reached this standing is owed to the enormous
progress which been made in developing more efficient algorithms for dynamical
fermions, better discretizations, as well as a number of new theoretical concepts
such as non-perturbative renormalization. These developments, in conjunction
with the availability of ever more powerful computers, shall allow for precise
computations of many phenomenologically relevant quantities, which previously
seemed virtually intractable.
5.9 Addendum: QCD on the Lattice
5.9.1 Introduction
Since the first edition of this article [241] the field of lattice QCD has undergone
a huge transformation. While the actual methodology was well established at
the time of writing (2007), few simulations employing dynamical quarks had
produced results with controlled errors, having a direct impact on phenomenology
and experiment. During the past ten years or so this has changed dramatically.