Continued from Fermilab Today, August 10, 2005
The most promising approach has been to formulate QCD on a space-time lattice. In the last couple of years, the promise has begun to be realized, with several calculations agreeing with previously measured properties of mesons and baryons. Members of Fermilab's Theoretical Physics Department and Computing Division, together with the MILC Collaboration, decided to extend their earlier work to take up CLEO-c's challenge. In a paper submitted to Physical Review Letters on June 28, their calculation resulted in a prediction:
ƒD = 201 ± 17 MeV,
where the uncertainty arises from various sources, such as the fact that the calculation is done on a lattice rather than in continuous space-time.
CLEO-c collected events in which an e+e- pair annihilates to form a charm—anti-charm bound state called ψ (3770). The ψ (3770) subsequently decays into D+D- pairs. The CLEO experimenters can then use one D meson as a tag to count the leptonic decays of the other. They announced their result on July 1, at the Lepton-Photon conference, reporting:
ƒD = 223 ± 18 MeV,
where the uncertainty is mostly statistical, i.e., from random fluctuations in the number of leptonic decays counted during the course of the experiment.
Given the uncertainties, the lattice-QCD calculation correctly predicted the measurement. The theorists are now carrying out further calculations to make their result more precise, while CLEO continues to run, collecting more D decays to reduce the statistical error. Next year we shall see if the theorists can pass an even more stringent test.
The D-meson decay constant is not the first aspect of D decay to exhibit agreement between a prediction from lattice QCD and an experiment. Last year, the same team of theorists considered the semileptonic decay of the D meson. Two months later Fermilab's FOCUS experiment measure the shape of the semileptonic form factor, and found agreement with the lattice QCD calculation.