Lattice QCD at the frontiers

Global fit to experimental flavor measurements combined with Standard Model theory, known as the CKM unitarity triangle. Deviations from the CKM paradigm would manifest themselves as inconsistencies between the colored bands. The bands labeled εK +|Vcb|, |Vub|/|Vcb|, ΔMs/ΔMd , and BR(B → τν) +ΔMBs all use results from the Fermilab Lattice Collaboration. Figure courtesy of Enrico Lunghi

Precision measurements of processes that are expected to be rare in the Standard Model provide powerful probes of new physics. Conjectured new heavy particles may contribute to these processes and be observed as deviations from Standard Model expectations. For many of these quantities, numerical lattice quantum chromodynamics calculations are needed for accurate theoretical predictions, thereby maximizing the scientific impact of current and future experimental measurements.

Lattice QCD provides the only first-principles method for calculating, with controlled errors, the properties of particles containing quarks by casting the basic equations of QCD into a form amenable to high-performance computing. Since 2006, the U.S. lattice community has received essential hardware and software funding from the DOE High Energy and Nuclear Physics program offices. Fermilab has provided leadership for this project, particularly in the design and operation of dedicated high-performance parallel computers for lattice QCD.

In 2003, teraflop-scale processing power and improved computing algorithms enabled the first realistic lattice QCD calculations, including the effects of dynamical up, down and strange quarks. The methodology of lattice QCD has since been validated by comparison with a broad array of measured quantities. For example, in 2005, the Fermilab Lattice Collaboration and colleagues correctly predicted the mass of the Bc meson before it was measured by CDF.

A decade ago, the heavy-flavor factories and Tevatron Run II were beginning precision studies of charm and bottom quarks to test the Cabibbo-Kobayashi-Maskawa paradigm, which describes the weak interactions of quarks. Concurrently, the Fermilab Lattice Collaboration embarked upon an ambitious program to calculate B and D meson parameters needed to interpret the experimental heavy-flavor results as elements of the CKM matrix. These and other lattice results played an important role in establishing that the CKM paradigm describes the weak interactions of quarks to within about 10 percent. This momentous confirmation led to the share of the 2008 Nobel Prize in physics for Kobayashi and Maskawa.

To this day, the Fermilab Lattice Collaboration continues to be a leader in lattice QCD calculations to search for new quark flavor-changing interactions. We are now also expanding our physics program to provide lattice calculations needed to support future Energy and Intensity frontier experiments, focusing especially on those planned to run at Fermilab. Some examples are calculating the hadronic light-by-light contribution to the muon g-2, which is needed to solidify and improve the Standard Model prediction and interpret the upcoming measurement as a search for new physics; calculating the nucleon axial form factor, which is needed to improve determinations of neutrino interactions with protons and neutrons relevant for accelerator-based neutrino experiments such as LBNE; and improving calculations of the masses of the charm and bottom quarks and the strong coupling constant, which are needed to sharpen predictions of the different ways the Higgs can decay.

We hope that in the coming years precision measurements will definitively establish the presence of physics beyond the Standard Model, with lattice QCD calculations playing a key role.

Ruth Van de Water

The Fermilab Lattice Collaboration includes the following members of the Fermilab Theory Group. Top row, from left: Andreas Kronfeld, Paul Mackenzie. Bottom row, from left: Jim Simone, Ruth Van de Water. Not shown: Daniel Mohler and Ran Zhou.