Most Precise Mass Calculation For Lattice QCD

A team of theoretical physicists have produced the best prediction of a particle’s mass. And within days of their paper being submitted to Physical Review Letters, that very particle’s mass was accurately measured at Fermilab, providing striking confirmation of the predicted value. How do the known particles acquire the mass they have? The answer might come from lattice QCD, the name for a computational approach to understanding how quarks interact.

Imagine quarks placed at the interstices of a crystal-like structure. Then let the quarks interact with each other via the exchange of gluons along the links between the quarks. The gluons are the designated carriers of the strong nuclear force under the general auspices of the theory called quantum chromodynamics (QCD). From this sort of framework the mass of the known hadrons (quark-containing composite particles such as mesons and baryons) can be calculated.

Until recently, however, the calculations were marred by a crude approximation. A big improvement came only in 2003, when uncertainties in mass predictions went from the 10% level to the 2% level (see Davies et al., Physical Review Letters, 16 January 2004). The mass of the proton, for example, could be calculated within a few percent of the actual value. Progress has come from a better treatment of the light quarks and from greater computer power.

Together the improvements provide the researchers with a realistic treatment of the "sea quarks," the virtual quarks whose ephemeral presence has a noticeable influence over the "valence" quarks that are considered the nominal constituents of a hadron. A proton, for example, is said to consist of three valence quarks---two up quarks and one down quark---plus a myriad of sea quarks that momentarily pop into existence in pairs. Now, for the first time, the mass of a hadron has been predicted with lattice QCD.

Andreas Kronfeld (ask@fnal.gov, 630-840-3753) and his colleagues at Fermilab, Glasgow University, and Ohio State report a mass calculation for the charmed B meson (Bc, for short, consisting of an anti-bottom quark and a charmed quark). The value they predict is 6304 +/- 20 MeV---the remarkable precision stems not only from the improvements discussed above, but also from the researchers' methods for treating heavy quarks. A few days after they submitted their Letter for publication, the first good experimental measurement of the same particle was announced 6287 +/- 5 MeV.

This successful confirmation is exciting, because it bolsters confidence that lattice QCD can be used to calculate many other properties of hadrons. (Allison et al., Physical Review Letters,6 May 2005; Lattice QCD website at http://lqcd.fnal.gov/)