The Standard Model of particle physics is remarkably successful in
describing the observed fundamental particles and their interactions
at the level of precision we have been able to probe thus far in
experiments. Despite this, there are several reasons to expect
that it is only the lowenergy (longdistance) description of
a more fundamental theory. The Standard Model fails to explain
certain observed experimental phenomena such as the matterantimatter
imbalance, dark matter and dark energy, and neutrino masses. It also
leaves important theoretical questions unanswered, such as the origin
of the particle masses and mixing parameters. Thus the foremost
goal of the experimental highenergy physics program is to search
for direct and indirect signs of new particles and forces.
Many experiments aim to search for quantummechanical effects of
new particles that give rise to tiny deviations from StandardModel
expectations. Maximizing the newphysics discovery potential of these
highprecision experiments requires reliable and equally precise
theoretical predictions. In almost all cases, the precision
of these tests are limited by our knowledge of the effects of the
strong interaction (QCD) on weakinteraction processes. Numerical
latticeQCD simulations provide the only method for calculating the
needed hadronic matrix elements and parameters of the QCD Lagrangian
with controlled uncertainties that are systematically improvable.
The objective of USQCD is to bring the latticeQCD errors down to,
or below, the experimental ones.
Compilation of latticeQCD calculations of meson and baryon masses
(update of Kronfeld 2012).
Over the past decade, increased computing power and better algorithms
have led to substantial progress in the latticeQCD computations of
quantities needed to interpret experimental results in the areas of
particle physics, nuclear physics, and even astrophysics. It is now
standard in latticeQCD simulations to include the full effects of
vacuum polarization due to light (up, down and strange) quarks, and to
simulate with pion masses close to the value in Nature. LatticeQCD
calculations successfully reproduce the experimentallymeasured
lowlying hadron spectrum, as shown in the figure at right.
Lattice QCD provides the most precise determination of the strong
coupling constant, α_{s}, and competitive
determinations of the charmand bottomquark masses. Further,
latticeQCD calculations correctly predicted the mass of the
B_{c} meson, the leptonic decay constants
f_{D} and f_{Ds}, and the
D → Klν semileptonic form factor
before the availability of precise
experimental measurements. These successful predictions and
postdictions validate the methods of numerical lattice QCD, and
demonstrate that reliable results can be obtained with controlled
uncertainties.
Lattice QCD has matured into a precision tool for quarkflavor
physics. Results with fully controlled errors are available for
nearly twenty matrix elements. By contrast, in 2007, only the
ratio of kaontopion decay constants,
f_{K}/f_{π},
was fully controlled.
The figure at left shows a recent compilation of latticeQCD results for the
D and D_{s}meson
decay constants. There are now several calculations with controlled
uncertainties using different lattice quark and gluon actions, which
provide independent confirmation. The most precise calculations
are from USQCD with errors of 0.6% and 0.5% on
f_{D} and f_{Ds},
respectively, use a highlyimproved charmquark lattice action and
include physicalmass pions. In the corresponding determinations of the
CabibboKobayashiMaskawa (CKM) quarkmixing matrix elements
V_{cd} and V_{cs},
the latticeQCD errors are now below the experimental errors.
Constraints on the CabibboKobayashiMaskawa quarkmixing matrix.
LatticeQCD calculations are essential to obtain constraints from
neutral kaon mixing (lilac band) and neutral
B_{d} and B_{s}meson
mixing (green band), and also enable
determinations of the CKM matrix elements
V_{ub}/V_{cb}
(bright yellow band). Recent lattice
results have significantly tightened the constraints and increased
the tension between them.
Recently, members of USQCD have produced new latticeQCD results
for the B → pi and
B → K semileptonic form factors,
the B → Dlν
form factor at nonzero recoil, the ratio of
Λ_{b} → Λ_{c}lν/Λ_{b} → plν
form factors, and the neutral
B_{d} and B_{s}meson
mixing matrix elements. These calculations
led to significant improvements in the determinations of the
CabibboKobayashiMaskawa (CKM) quarkmixing matrix elements
V_{ub},
V_{cb},
V_{td}, and
V_{ts}. The figure at right
shows constraints on the CKM matrix using the
latest latticeQCD inputs. In this plot, newphysics effects would
show up as inconsistent constraints on the apex
(ρ
,η)
of the unitarity triangle. These recent latticeQCD calculations
substantially tightened several of the constraints and reduced the
allowed StandardModel parameter space. They also confirmed and/or
revealed several tensions with the Standard Model of about 2 standard
deviations in the quarkflavor sector.
USQCD is devoting considerable human effort and computing resources
to meet the theory needs of current and upcoming highenergy
physics experiments. Petascale computing is enabling better
simulations with physicalmass pions, very fine lattice spacings,
very large volumes, and dynamical charm quarks, all of which will
lead to increase precision on present calculations. The precision
on simple quantities is approaching the level where strongisospin
breaking and electromagnetic corrections are becoming relevant.
Simulating with different up and downquark masses straightforward.
Methods for are being developed to include electromagnetism in
lattice simulations, and lattice QCD can already reproduce simple
quantities such as the neutronproton mass difference. USQCD is also
targeting more challenging quantities needed by current and future
experiments. Recently members of USQCD achieved the first complete
QCD calculations of the mass difference between kaon eigenstates,
which is a longdistance amplitude, and of the matrix elements
for K → ππ decays, which has multiple hadrons in the final state.
They also presented the first proofofprinciple demonstration of
a method to calculate the lightbylight contribution to the muon
anomalous magnetic moment (g−2). Continued efforts in developing
new theoretical methods and better algorithms are ongoing. In the
coming decade, anticipated progress in latticeQCD calculations plus
new experimental measurements will continue to increase the precision
on StandardModel parameters and sharpen tests of the Standard Model,
hopefully revealing definitive evidence of physics beyond.
