Hans Fischer Senior Fellow, Technische Universität München

We carry out a wide variety of lattice-QCD calculations needed to interpret experiments in particle physics.
Many of these are calculations of *B*-, *D*-, and *K*-meson decay and mixing amplitudes, needed to determine the pattern of flavor mixing.
Some of these calculations are more oriented to determining the flavor couplings of the Standard Model.
Others, in a complementary way, focus on processes that are expected to be sensitive to interactions beyond the Standard model.
Further, closely related calculations provide information on the quarks masses.
Most of these experiments are (nowadays) located abroad:
LHC*b* at CERN,
Belle II at KEK,
BES III at IHEP Beijing,
KOTO at J-PARC, and NA62 at CERN.

The experimental program at Fermilab includes many experiments with oriented to the properties of leptons.
One might think, therefore, that the strong interactions (of quarks and gluons) play a minor role.
The sensitivity of these experiments, however, means the QCD effects must still be calculated.
For example, the uncertainty on the hadronic contributions to the anomalous magnetic moment of the muon must be improved
by at least a factor of four in order to learn as much as possible from the
Muon *g*−2 Experiment.
Several nucleon matrix elements (analogous to those discussed above for mesons) are needed to understand neutrino scattering and, hence, measurements of neutrino mixing parameters.
These phenomena are measured in several experiments
MiniBooNE and MicroBooNE,
MINOS and MINOS+,
MINERνA,
NOνA, and
the future Long Baseline Neutrino Facility (LBNF).
Related calculations are useful for setting limits in muon-to-electron conversion, which is studied by the
Mu2e Experiment,
and direct dark matter detection, which is studied by (for a Fermilab examples)
COUPP and
(Super)CDMS.

Problems of many length scales present some of the greatest challenges in physics. Our Focus Group nurtures two of the most powerful theoretical tools and brings them together in a fruitful way. The key, of course, to problems with many length scales is the renormalization group, particularly in the form developed by Kenneth Wilson in the 1970s, which shows how how to set up a chain of so-called effective quantum field theories, each of which holds—or is “effective”—over a narrower range of scale. Around the same time, Steven Weinberg introduced a related concept, in which the symmetries of a system are exploited to constrain the effective theory. Taken together, the two forms of effective field theory provide a tractable framework, such that the best theoretical (or computational) tool can be brought to bear at each scale.

One such tool is lattice gauge theory, which formulates quantum field theory on a grid in space or, more commonly, space and time. We will develop effective field theories in a way that will allow more problems to be addressed with lattice gauge theory. Our main focus will be on quantum chromodynamics (QCD), with applications of interest to particle physics, nuclear physics, and astrophysics. Recently, a connections between lattice gauge theory and cold atoms in optical lattices has been discovered, and we plan to work in this area too.