High-Precision Lattice QCD Confronts Experiment

The recently developed Symanzik-improved staggered-quark discretization allows unquenched lattice-QCD simulations with much smaller (and more realistic) quark masses than previously possible. To test this formalism, we compare experiment with a variety of nonperturbative calculations in QCD drawn from a restricted set of “gold-plated” quantities. We find agreement to within statistical and systematic errors of $3\%$ or less. We discuss the implications for phenomenology and, in particular, for heavy-quark physics.

Figure 1

LQCD results divided by experimental results for nine different quantities, without and with quark vacuum polarization (left and right panels, respectively). The top three results are from our $a=1/11$ and $1/8\mathrm{f}\mathrm{m}$ simulations; all others are from $a=1/8\mathrm{f}\mathrm{m}$ simulations.

Figure 2

Chiral fits to LQCD determinations of $f_{\pi }$ and $f_K$ (in GeV) for different values of the valence $u/d$-quark mass at $a=1/11\mathrm{f}\mathrm{m}$.

Figure 3

Gold-plated LQCD processes that bear on CKM matrix elements. ${ϵ}_K$ is another gold-plated quantity.