Lattice QCD should allow quantitative predictions for the heavy quark physics from first principles. Up to now, however, most approaches have based on the nonrelativistic effective theory, with which the continuum limit can not be taken in principle. In this paper we investigate feasibility of relativistic approaches to the heavy quark physics in lattice QCD. We first examine validity of the idea that the use of the anisotropic lattice could be advantageous to control the $m_Q a$ corrections. Our perturbative calculation, however, reveals that this is not true. We instead propose a new relativistic approach to handle heavy quarks on the isotropic lattice. We explain how power corrections of $m_Q a$ can be avoided and remaining uncertainties are reduced to be of order $(a\Lambda_{QCD})^2$.Comment: 39 pages, 8 figure as eps-fil

We report results of quark masses in quenched lattice QCD with the Kogut-Susskind fermion action, employing the regularization independent scheme of Martinelli et al. to nonperturbatively evaluate the renormalization factor relating the bare quark mass on the lattice to that in the continuum. Calculations are carried out at b 6.0, 6.2, and 6.4, from which we find m

We present a model-independent calculation of hadron matrix elements for all dimension-6 operators associated with baryon number violating processes using lattice QCD. The calculation is performed with the Wilson quark action in the quenched approximation at ␤ϭ6/g 2 ϭ6.0 on a 28 2 ϫ48ϫ80 lattice. Our results cover all the matrix elements required to estimate the partial lifetimes of ͑proton,neutron͒→(,K,) ϩ( ,e ϩ , ϩ ) decay modes. We point out the necessity of disentangling two form factors that contribute to the matrix element; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which could give strong constraints on several GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of the chiral Lagrangian.

We present a high statistics study of the light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks. Numerical simulations are carried out using the plaquette gauge action and the O(a)-improved Wilson quark action at ␤ϭ5.2, where the lattice spacing is found to be aϭ0.0887(11) fm from the meson mass, on a 20 3 ϫ48 lattice. At each of five sea quark masses corresponding to m PS /m V Ӎ0.8-0.6, we generate 12 000 trajectories using a symmetrically preconditioned Hybrid Monte Carlo algorithm. Finite spatial volume effects are investigated employing 12 3 ϫ48, 16 3 ϫ48 lattices. We also perform a set of simulations in quenched QCD with the same lattice actions at a similar lattice spacing to those for the full QCD runs. In the meson sector we find clear evidence of sea quark effects. The J parameter increases for lighter sea quark masses, and the full QCD meson masses are systematically closer to experiment than in quenched QCD. Careful finite-size studies are made to ascertain that these are not due to finite-size effects. Evidence of sea quark effects is less clear in the baryon sector due to larger finite-size effects. We also calculate light quark masses and find m ud MS (2 GeV)ϭ3.223(Ϫ0.069 ϩ0.046) MeV and m s MS (2 GeV)ϭ84.5(Ϫ1.7 ϩ12.0) MeV which are about 20% smaller than in quenched QCD.

We present a polynomial hybrid Monte Carlo ͑PHMC͒ algorithm for lattice QCD with odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm makes use of the non-Hermitian Chebyshev polynomial to approximate the inverse square root of the fermion matrix required for an odd number of flavors. The systematic error from the polynomial approximation is removed by a noisy Metropolis test for which a new method is developed. Investigating the property of our PHMC algorithm in the N f ϭ2 QCD case, we find that it is as efficient as the conventional HMC algorithm for a moderately large lattice size (16 3 ϫ48) with intermediate quark masses (m PS /m V ϳ0.7-0.8). We test our odd-flavor algorithm through extensive simulations of two-flavor QCD treated as an N f ϭ1ϩ1 system, and comparing the results with those of the established algorithms for N f ϭ2 QCD. These tests establish that our PHMC algorithm works on a moderately large lattice size with intermediate quark masses (16 3 ϫ48,m PS /m V ϳ0.7-0.8). Finally we experiment with the (2 ϩ1)-flavor QCD simulation on small lattices (4 3 ϫ8 and 8 3 ϫ16), and confirm the agreement of our results with those obtained with the R algorithm and extrapolated to a zero molecular dynamics step size.