Lattice QCD calculations make possible constraints on the CKM matrix from K anti-K meson mixing
(light green band), and from
B anti-B and Bs anti-Bs mixing (yellow and orange bands, respectively).
Despite its extraordinary success, the Standard Model is believed to be
only the low energy (long distance) limit of a more fundamental theory.
Therefore, a major component of the experimental program in high energy
physics is devoted to making precise tests of the Standard Model in order
to determine its range of validity and search for indications
of new physics beyond it. Many of these tests require both accurate
experiments and accurate lattice QCD calculations of the effects of
the strong interactions on weak interaction processes. In almost all
cases, the precision of the tests are limited by the uncertainties in
the lattice calculations, rather than in the experiments. Our objective
is to bring the lattice errors down to, or below, the experimental ones.
Theory compared with experiment in the quenched approximation and in full QCD.
Shape of the form factor for the decay of a D meson into a kaon and leptons
predicted by lattice QCD (orange band) and measured by experiment (purple diamonds).
The greatest challenge to performing accurate numerical calculations
of QCD is to include the full effects of vacuum polarization due to light
(up, down and strange) quarks. Significant progress has been made in
meeting this challenge during the past five years through the use of
improved formulations of QCD on the lattice and through rapid growth in
the computing resources available to the field. This progress is illustrated
in the figure in the upper right in which the ratio of lattice results to experimental
results for a number of experimentally well determined quantities is plotted.
The panel on the left shows lattice results from the quenched approximation
in which vacuum polarization effects are neglected, while the panel on the
right shows lattice results for full QCD.
Other notable results include
calculations of mass splittings in the charmonium and bottomonium spectra,
the strong coupling constant and
the Cabibbo-Kobayashi-Maskawa (CKM) matrix
element Vus, to the same accuracy as their experimental determinations.
The lattice gauge theory community has moved from the validation of techniques
through the calculation of quantities that are well known experimentally to
the successful prediction of quantities that had not previously been measured.
Three cases in which predictions were subsequently confirmed by experiment
were the calculations of the leptonic decay constants of the D and Ds
mesons and the mass of the Bc meson. Another example was the successful
prediction of the form factor for the decay of the D meson into a K meson
and leptons, which is illustrated in the figure at the left. The orange band
is the lattice prediction and the blue plotting symbols are the results of
the Belle Collaboration.
These successes demonstrate that lattice gauge theorists are in a
position to make accurate determinations of a number of quantities crucial
to Standard Model tests, including amplitudes for the leptonic and
semi-leptonic decays of B mesons, and the mixing of neutral K and B mesons with their anti-particles. These calculations are in progress.
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