PHYSICAL RESULTS from PARTIALLY QUENCHED SIMULATIONS

For some time to come, simulations of lattice QCD will not work directly with physical up and down quarks. This is because the computer time required scales roughly as m q with existing algorithms (at fixed physical box size). Present simulations, using machines sustaining up to 0.3 Teraflops, are limited to quark masses greater than about half the strange quark mass, an order of magnitude larger than the average up and down quark mass. Even a dedicated machine sustaining 10 Teraflops (hopefully to be available in 2003-4) will allow quark masses to be reduced to only ∼ ms/8. Thus an extrapolation in light quark masses is required. Fortunately, this can be done, using chiral perturbation theory (ChPT), once the simulated masses are small enough. In practice, it is feasible to determine the functional forms with which to extrapolate at next-to-leading order (NLO) in the chiral expansion. A useful way of thinking about the extrapolation is that simulations with moderately light quark masses can be used to determine the parameters of the chiral Lagrangian (including the Gasser-Leutwyler coefficients L1−10 which appear at NLO), and then the extrapolation can be done “by hand”. In this talk we describe some recent work in which we show how the chiral extrapolation can be aided by the use of partially quenched (PQ) simulations. These are simulations in which the “valence” and “sea” (= “dynamical”) quarks have different masses. The key theoretical observation is that, if both valence and sea quarks are light enough, then the chiral Lagrangian describing the long distance properties of the PQ simulations contains the same parameters (f , 〈q̄q〉, and L1−10) as appear in the chiral Lagrangian for QCD . This follows from the work of Ref. . Thus one can extrapolate to the physical theory using PQ as well as unquenched simulations, without introducing new, unphysical, parameters. This is true despite the fact that the PQ theory itself is unphysical. The practical importance of this observation has yet to be seen, but could be significant. It is relatively cheap (CPU ∼ m V ) to reduce the valence quark masses