We discuss in general the construction of gauge-invariant non-local meson operators on the lattice. We use such operators to study the $P$- and $D$-wave mesons as well as hybrid mesons in quenched QCD, with quark masses near the strange quark mass. The resulting spectra are compared with experiment for the orbital excitations. For the states produced by gluonic excitations (hybrid mesons) we find evidence of mixing for non-exotic quantum numbers. We give predictions for masses of the spin-exotic hybrid mesons with $J^{PC}=1^{-+},\ 0^{+-}$, and $2^{+-}$.Comment: 31 pages, LATEX, 8 postscript figures. Reference adde

We measure the critical exponents of the three dimensional Gross-Neveu model with two four-component fermions. The exponents are inferred from the scaling behaviour of observables on lattice sizes 8 3 , 12 3 , 16 3 , 24 3 , and 32 3 . We find that the model has a second order phase transition with ν = 1.00(4) and 2 − η = γ/ν = 1.246(8). We also calculate these exponents, through a second order ǫ-expansion around four dimensions, for the three dimensional Higgs-Yukawa model, which is expected to be in the same universality class, and obtain γ/ν = 1.237 and ν = 0.948, while recent second order 1/N f -expansion calculations give γ/ν = 1.256 and ν = 0.903. We conclude that the equivalence of the two models remains valid in 3 dimensions at fixed small N f values.

We use lattice methods to evaluate from first principles the spectrum of hybrid mesons produced by gluonic excitations in quenched QCD with quark masses near the strange quark mass. For the spin-exotic mesons with J P C = 1 −+ , 0 +− , and 2 +− which are not present in the quark model, we determine the lightest state to be 1 −+ with mass of 2.0(2) GeV.One of the goals of quantitative studies of QCD is to determine the masses and properties of states which are not allowed in the simple quark model because they contain gluonic excitations. The prototype for such a state is the glueball and accurate lattice studies [1,2] have been able to pinpoint the relevant mass range for experimental study of the scalar glueball as around 1.6 GeV. Another important area is the study of hybrid mesons which are qq mesons with gluonic excitation. Because the gluonic excitation can introduce angular momentum, the most clear cut signal for a hybrid meson is to search for J P C quantum numbers not allowed in the quark model. These include J P C = 1 −+ , 0 +− , and 2 +− . Again lattice QCD is capable, from first principles, of establishing the masses of these states.In full QCD, the quark pair creation and anihilation processes will lead to the mixing of glueballs with qq mesons and it is thus appropriate to establish the glueball spectrum with these processes turned off -the quenched approximation. This then acts as a guide for mixing studies. For hybrid mesons, however, the quenched approximation already allows mixing between qq mesons and hybrid mesons if their J P C quantum numbers are non-exotic. This will be quite difficult to untangle in lattice studies, so we focus instead on the exotic J P C cases. Any mixing for these exotic J P C states would have to be with qqqq mesons and such mixing is turned off in the quenched approximation. Thus, in the quenched approximation, we are able 1

We analyse the meson spectrum in quenched QCD using lattice gauge theory. By studying hadron propagation with a variety of operators (both smeared and local), we are able to extract the ground state and first excited state masses with confidence. We pay attention to the correlations among the data used in the fits to extract these masses and couplings. We compare the resulting hadron spectrum with experiment and find evidence for a significant departure in the pseudoscalar and vector meson masses.

We calculate connected and disconnected contributions to the flavour singlet scalar density amplitude of the nucleon in a full QCD lattice simulation with n f = 2 dynamical Wilson fermions at β = 5.6 on a 16 3 × 32 lattice. We find that both contributions are of similar size at the light quark mass. We arrive at the estimate σ πN = 18(5)MeV. Its smallness is directly related to the apparent decrease of u, d quark masses when unquenching QCD lattice simulations. The y parameter can be estimated from a semi-quenched analysis, in which there are no strange quarks in the sea, the result being y = 0.59(13).