Search

By numerical study of the simple bound states of light quarks, in particular the π and K mesons, we are able to deduce fundamental quark properties. Using the "improved staggered" discretization of QCD, the MILC Collaboration has performed a series of simulations of these bound states, including the effects of virtual quark-antiquark pairs ("sea" quarks). From these simulations, we have determined the masses of the up, down, and strange quarks. We find that the up quark mass is not zero (at the 10 sigma level), putting to rest a twenty-year-old suggestion that the up quark could be massless. Further, by studying the decays of the π and K mesons, we are able to determine the "CKM matrix element" Vus of the Weak Interactions. The errors on our result for Vus are comparable to the best previous determinations using alternative theoretical approaches, and are likely to be significantly reduced by simulations now in progress.

We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move. This is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover at any nonzero density, and that at low enough temperature chiral symmetry remains broken at all densities.

A calculation of the ratio of leptonic decay constants f(K+)/f(π+) makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V(us)|/|V(ud)| in the standard model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute f(K+)/f(π+) numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings a ≈ 0.06, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain f(K+)/f(π+) = 1.1947(26)(37), where the errors are statistical and total systematic, respectively. This is our first physics result from our N(f) = 2+1+1 ensembles, and the first calculation of f(K+)/f(π+) from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f(K+)/f(π+), with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of |V(us)|/|V(ud)| = 0.2309(9)(4) where the errors are theoretical and experimental, respectively.