Reduced critical slowing down for statistical physics simulations.

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode," which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We first demonstrate supercritical slowing down in a phase with spontaneously broken symmetry and for the heat-bath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetization as collective coordinate, we present evidence that supercritical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is, however, reduced by orders of magnitude when compared to local update techniques.

Nucleon Structure Functions from Operator Product Expansion on the Lattice.

Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

Electric Dipole Moment of the Neutron from 2+1 Flavor Lattice QCD.

We compute the electric dipole moment d(n) of the neutron from a fully dynamical simulation of lattice QCD with 2+1 flavors of clover fermions and nonvanishing θ term. The latter is rotated into a pseudoscalar density in the fermionic action using the axial anomaly. To make the action real, the vacuum angle θ is taken to be purely imaginary. The physical value of dd(n) is obtained by analytic continuation. We find d(n)=-3.9(2)(9)×10(-16) θ e cm, which, when combined with the experimental limit on d(n), leads to the upper bound |θ|≲7.4×10(-11).

Determination of the strange nucleon form factors.

The strange contribution to the electric and magnetic form factors of the nucleon is determined at a range of discrete values of Q^{2} up to 1.4 GeV^{2}. This is done by combining a recent analysis of lattice QCD results for the electromagnetic form factors of the octet baryons with experimental determinations of those quantities. The most precise result is a small negative value for the strange magnetic moment: G_{M}^{s}(Q^{2}=0)=-0.07±0.03µ_{N}. At larger values of Q^{2} both the electric and magnetic form factors are consistent with zero to within 2 standard deviations.

Strangeness contribution to the proton spin from lattice QCD.

We compute the strangeness and light-quark contributions Δs, Δu, and Δd to the proton spin in n(f)=2 lattice QCD at a pion mass of about 285 MeV and at a lattice spacing a≈0.073 fm, using the nonperturbatively improved Sheikholeslami-Wohlert Wilson action. We carry out the renormalization of these matrix elements, which involves mixing between contributions from different quark flavors. Our main result is the small negative value Δs(MS)(√(7.4) GeV)=-0.020(10)(4) of the strangeness contribution to the nucleon spin. The second error is an estimate of the uncertainty, due to the missing extrapolation to the physical point.

Electroproduction of the N*(1535) resonance at large momentum transfer.

We report on the first lattice calculation of light-cone distribution amplitudes of the N*(1535) resonance, which are used to calculate the transition form factors at large momentum transfers using light-cone sum rules. In the region Q2>2 GeV2, where the light-cone expansion is expected to converge, the results appear to be in good agreement with the experimental data.

Spin structure of the pion.

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.

Transverse spin structure of the nucleon from lattice-QCD simulations.

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.

Generalized parton distributions from lattice QCD.

We perform a quenched lattice calculation of the first moment of twist-two generalized parton distribution functions of the proton, and assess the total quark (spin and orbital angular momentum) contribution to the spin of the proton.

Calorons and localization of quark eigenvectors in lattice QCD.

We analyze the localization properties for eigenvectors of the Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition. Studying the characteristic differences between the Z3 sectors above the critical temperature T(c), we find indications for the presence of calorons.

Lens/cornea relationships: the key to fine-tuning soft lens fits.

Currently, it is rare to be unable to fit a patient with spherical soft lenses, and it is becoming increasingly easy to [figure: see text] achieve success with toric and other specialty lenses. If we fulfill the criteria of full corneal coverage, acceptable movement, overrefraction to a clear end point, and stable, nonfluctuating visual acuity, our patients should be well on their way to long-term success with soft lenses.