We report on a lattice QCD calculation of the strangeness magnetic moment of the nucleon. Our result is G s M (0) = −0.36 ± 0.20. The sea contributions from the u and d quarks are about 80% larger. However, they cancel to a large extent due to their electric charges, resulting in a smaller net sea contribution of −0.097 ± 0.037µ N to the nucleon magnetic moment. As far as the neutron to proton magnetic moment ratio is concerned, this sea contribution tends to cancel out the cloud-quark effect from the Z-graphs and result in a ratio of −0.68 ± 0.04 which is close to the SU(6) relation and the experiment. The strangeness Sachs electric mean-square radius r 2 s E is found to be small and negative and the total sea contributes substantially to the neutron electric form factor.

We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from the overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e. consisting of connected sign-coherent regions with local dimensions 1 ≤ d < 4, and spreading over arbitrarily large spacetime distances. Here we show that the space-time structure responsible for the origin of topological susceptibility indeed exhibits global behavior. In particular, we show numerically that topological fluctuations are not saturated by localized concentrations of most intense topological charge density. To the contrary, the susceptibility saturates only after the space-time regions with most intense fields are included, such that geometrically global structure is already formed. We demonstrate this result both at the fundamental level (full topological density) and at low energy (effective density). The drastic mismatch between the point of fluctuation saturation (≈ 50% of space-time at low energy) and that of global structure formation (< 4% of space-time at low energy) indicates that the ordered space-time structure in topological charge is inherently global and that topological charge fluctuations in QCD cannot be understood in terms of individual localized pieces. Description in terms of global brane-like objects should be sought instead.

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is ≈ 2 a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part.

We study the a 0 and mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the 0 ghost states are separated, we find the a 0 mass with the q q interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with a 0 1450 being the u d meson and K 0 1430 being the u s meson with calculated masses at 1:42 0:13 GeV and 1:41 0:12 GeV, respectively. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two-pion scattering states, we find a state at 550 MeV. Through the study of volume dependence, we confirm that this state is a one-particle state, in contrast to the two-pion scattering states. This suggests that the observed state is a tetraquark mesonium which is quite possibly the 600 meson.

The overlap fermion propagator is calculated on 2 + 1 flavor domain wall fermion gauge configurations on 16 3 × 32, 24 3 × 64 and 32 3 × 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ∼ 20 times for the 16 3 × 32 lattice and ∼ 80 times for the 32 3 × 64 lattice. The overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices. Through the study of hyperfine splitting, we found that the O(m 2 a 2 ) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. A preliminary calculation of the low energy constant ∆ mix which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is carried out via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ∼ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. We introduce a new algorithm with Z 3 grid source and low eigenmode substitution to study the the many-to-all meson and baryon correlators. It is found to be efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z 3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m π ∼ 200 − 300 MeV) meson and nucleon correlators by a factor of ∼ 3 − 4 as compared to the point source. The Z 3 grid source itself can reduce the errors of the charmonium correlators by a factor of ∼ 3.