Lattice Quantum Chromodynamics

We present a calculation of the strangeness and charmness contents N |ss|N and N |cc|N of the nucleon from dynamical lattice QCD with 2 + 1 flavors. The calculation is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations. The configurations are generated by the RBC collaboration on a 24 3 × 64 lattice with sea quark mass am l = 0.005, am s = 0.04, and inverse lattice spacing a −1 = 1.73 GeV. Both actions have chiral symmetry which is essential in avoiding contamination due to the operator mixing with other flavors. Nucleon propagator and the quark loops are both computed with stochastic grid sources, while low-mode substitution and low-mode averaging methods are used respectively which substantially improve the signal to noise ratio. We obtain the strangeness matrix element f Ts = m s N |ss|N /M N = 0.0334(62), and the charmness content f Tc = m c N |cc|N /M N = 0.094(31) which is resolved from zero by 3 σ precision for the first time.

We report on our implementation of the RHMC algorithm for the simulation of lattice QCD with two staggered flavors on Graphics Processing Units, using the NVIDIA CUDA programming language. The main feature of our code is that the GPU is not used just as an accelerator, but instead the whole Molecular Dynamics trajectory is performed on it. After pointing out the main bottlenecks and how to circumvent them, we discuss the obtained performances. We present some preliminary results regarding OpenCL and multiGPU extensions of our code and discuss future perspectives.

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a cru

We evaluate all two-point correlation functions of the Curci-Ferrari (CF) model in four dimensions and in the presence of degenerate fundamental quark flavors. We compare our results to QCD lattice data in the two flavor case for two different values of the pion mass, one that is relatively far from the chiral limit, and one that is closer to the physical value. This work is a natural extension of an earlier investigation in the quenched approximation. Our results confirm that the QCD gluon and ghost dressing functions are well described by a perturbative approach within the CF model. As for the quark sector, our main result is that the quark dressing function is also well captured by the perturbative approach, but only starting at two-loop order, as anticipated in Ref.~\cite{Pelaez:2014mxa}. The quark mass function is also well reproduced if the quarks are not too light. As is well known, this function cannot be described within a purely perturbative approach in the case of too lig...

We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The calculation is carried out on a 16 3 × 24 quenched lattice at β = 6.0 and for Wilson fermions with κ = 0.154, 0.155, and 0.1555 which correspond to pion masses at 650, 538, and 478 MeV. The quark loops are calculated with Z 4 noise and signal-to-noise is improved further with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The u and d quark momentum/angular momentum fraction is 0.66(5)/0.72(5), the strange momentum/angular momentum fraction is 0.024(6)/0.023(7), and that of the glue is 0.31(6)/0.25(8). The orbital angular momenta of the quarks are obtained from subtracting the quark spins from the corresponding angular momentum components. As a result, the quark orbital angular momentum constitutes 0.50(2) of the proton spin, with almost all of it coming from the disconnected insertion. The quark spin carries a fraction 0.25(12) and glue carries a fraction 0.25(8) of the total proton spin.

Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) able to encompass a large number of processes within a unified framework. This allowed one to design a global fit procedure which provides a fair simultaneous description of the $$e^+ e^-$$e+e- annihilation into six final states ($$\pi ^+\pi ^-$$π+π-, $$\pi ^0\gamma $$π0γ, $$\eta \gamma $$ηγ, $$\pi ^+\pi ^-\pi ^0$$π+π-π0, $$K^+K^-$$K+K-, $$K_L K_S$$KLKS), the dipion spectrum in the $$\tau $$τ decay and some more light meson decay partial widths. In this paper, additional breaking schemes are defined which improve the BHLS working and extend its scope so as to absorb spacelike processes within a new framework ($${\hbox {BHLS}}_2$$BHLS2). The phenomenology previously explored with BHLS is fully revisited in the $${\hbox {BHLS}}_2$$BHLS2 context with special emphasis on the $$\phi $$ϕ mass region using all available data...

We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with Z 4 noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a 16 3 × 24 quenched lattice at β = 6.0 for Wilson fermions with κ = 0.154, 0.155, and 0.1555 which correspond to pion masses at 650, 538, and 478 MeV, respectively. The chirally extrapolated u and d quark momentum/angular momentum fraction is found to be 0.64(5)/0.70(5), the strange momentum/angular momentum fraction is 0.024(6)/0.023(7), and that of the glue is 0.33(6)/0.28(8). The previous study of quark spin on the same lattice revealed that it carries a fraction of 0.25(12) of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes 0.47(13) of the proton spin with almost all of it coming from the disconnected insertions.

The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector. In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector.

The four N to ∆ axial transition form factors are evaluated using quenched QCD, using two flavors of dynamical Wilson fermions and using domain wall valence fermions on three-flavor MILC configurations for pion masses down to 360 MeV. We provide a prediction for the parity violating asymmetry as a function of Q 2 and examine the validity of the off-diagonal Goldberger-Treiman relation. PoS(LAT2006)115

The mass of the 1-+ exotic meson, created with hybrid interpolating fields, is explored in numerical simulations of quenched QCD on large (20 3× 40) lattices to obtain good control of statistical and finite volume errors. Using the Fat-Link Irrelevant Clover (FLIC) fermion ...

We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincaré symmetry. We also study the concept of “quantum anomalous energy” proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.

We study the strangeness contribution to nucleon matrix elements using Nf=2+1 dynamical clover fermion configurations generated by the CP-PACS/JLQCD collaboration. In order to evaluate the disconnected insertion (DI), we use the Z(4) stochastic method, along with unbiased subtraction from the hopping parameter expansion which reduces the off-diagonal noises in the stochastic method. Furthermore, we find that using many nucleon sources for each configuration is effective in improving the signal. Our results for the quark contribution to the first moment _q in the DI, and the strangeness magnetic moment show that the statistical errors are under control with these techniques. We also study the gluonic contribution to the nucleon using the overlap operator to construct the gauge field tensor, F_{mu,nu}. The application to the calculation of first moment, _G, gives a good signal in quenched lattice QCD.

By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the derivative expansion of the general nucleon-nucleon potential U (r, r ′) = V (r, ∇r)δ 3 (r −r ′) is studied. The relative kinetic energy between two nucleons is introduced through the anti-periodic boundary condition in the spatial directions. On a hypercubic lattice with the lattice spacing a ≃ 0.137 fm and the spatial extent Ls ≃ 4.4 fm with the pion mass mπ ≃ 530 MeV, the local potentials for two different energies (E ≃ 0 MeV and 45 MeV) are compared and found to be identical within statistical errors, which validates the local approximation of U (r, r ′) up to E = 45 MeV for the central and tensor potentials. Central potentials in the spin-singlet channel for different orbital angular momentums (ℓ = 0 and ℓ = 2) at E ≃ 45 MeV are also found to be the same within the errors, which also supports the local approximation.

We have run a computer simulation in SU(2) lattice gauge theory on a 83 × 2 lattice including dynamical quark loops. No rapid variation is observed in the value of the Polyakov line, while the energy densities of quark and gluon show a strong indication of a second order phase transition around T ~ 250 MeV. In order to reduce finite size effects, the results are compared with those of a free gas on a lattice of the same size. The quark and gluon energy densities overshoot the free gas values at high temperature. The effect of the chemical potential is also studied. The behaviors of the energy densities and of the number density are fax from the free gas ease.

We present a formula for reducing the rank of Wilson fermions from 4NcNxNyNzNt to 4NcNxNyNz keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients Cn in the fugacity expansion of the fermion determinant n Cn(exp(µ/T)) n , which play an important role in the canonical formulation, using lattice QCD configurations on a 4 4 lattice. Numerically, log |Cn| varies as NxNyNz, and goes easily over the standard numerical range; We give a simple cure for that. The phase of Cn correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.

We evaluate the N to Delta axial transition form factors in lattice QCD in the quenched theory, with two degenerate flavors of dynamical Wilson fermions and using domain wall valence fermions with staggered sea quark configurations. We predict the ratio $C_5^A(q^2)/C_3^V(q^2)$ relevant to the parity violating asymmetry and check the validity of the off-diagonal Goldberger-Treiman relation.

We evaluate the N to ∆ axial transition form factors in lattice QCD with no dynamical sea quarks, with two degenerate flavors of dynamical Wilson quarks, and using domain wall valence fermions with three flavors of staggered sea quarks. We predict the ratio C A 5 (q 2)/C V 3 (q 2) relevant for parity violating asymmetry experiments and verify the off-diagonal Goldberger-Treiman relation.

We evaluate the nucleon axial form factor, GA(q 2), and induced pseudoscalar form factor, Gp(q 2), as well as the pion-nucleon form factor, GπNN (q 2), in lattice QCD. We also evaluate the corresponding nucleon to ∆ transition form factors, C A 5 (q 2) and C A 6 (q 2), and the pion-nucleon-∆ form factor GπN∆(q 2). The nucleon form factors are evaluated in the quenched theory and with two degenerate flavors of dynamical Wilson fermions. The nucleon to ∆ form factors, besides Wilson fermions, are evaluated using domain wall valence fermions with staggered sea quark configurations for pion masses as low as about 350 MeV. Using these form factors, together with an evaluation of the renormalized quark mass, we investigate the validity of the diagonal and non-diagonal Goldberger-Treiman relations. The ratios GπN∆(q 2)/GπNN (q 2) and 2C A 5 (q 2)/GA(q 2) are constant as a function of the momentum transfer squared and show almost no dependence on the quark mass. We confirm equality of these two ratios consistent with the Goldberger-Treiman relations extracting a mean value of 1.61(2).

We present a quenched lattice QCD calculation of the first few moments of the polarized and un-polarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing a −1 ≈ 1.3 GeV, physical volume V ≈ (2.4 fm) 3 , and light quark masses down to about 1/4 the strange quark mass (m π ≈ 400 MeV). Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of the flavor non-singlet momentum fraction to the helicity distribution, x u−d / x ∆u−∆ d , which is in very good agreement with experiment. We discuss the implications of this result. Next, we show that the chiral symmetry of domain wall fermions is useful in eliminating mixing of power divergent lower dimensional operators with twist-3 operators. Finally, we compute the isovector tensor charge at renormalization scale µ = 2 GeV in the M S scheme, 1 δu−δd = 1.192(30), where the error is the statistical error only.

Recent results obtained on the Columbia 64-node parallel supercomputer are reported_ The influence of many dynamical quark flavors on the finite temperature phase transition structure of lattice quantum chromodynamies (QCD) is investigated. ]:or the chosen numbers cf flavors, .~ : 8 and ~7, the pha~ structure is mapped out in the range of quark mass 0_1 < mqa ~ 10 on a ]6 ~ ~" 4 lattice with zer~ baryon density. In contrast to an earlier study, our resu!ts suggest that the chira~ and deconfinement phase transitions correspond to separate domains on the (~,q~ Nj) plane. For the two values of flavors studied, there is no qualitative d~erence in the phase structure_ Although the chiraJ transition becomes stronger with increasing JVj,, the phase structure is similar to that of N~ = 4 case_

We discuss technical aspects and first results of a lattice QCD study of the a 0 (980) state. We employ various interpolating operators of quark-antiquark, mesonic molecule, diquark-antidiquark and two-meson type. Both connected and disconnected contributions including diagrams with closed fermion loops are computed. To keep statistical errors small, it is essential to optimize the computation of these diagrams by choosing that combination of techniques most appropriate for each type of diagram from the correlation matrix of interpolating operators. We illustrate, how this can be done, by discussing certain diagrams in detail. We also present preliminary results corresponding to a 4 × 4 submatrix computed with 2+1 flavors of clover fermions.

The Feynman-Hellmann Theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including non-zero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time-dependence of the ground state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial-charge using gradient-flowed domain-wall valence quarks on the N f = 2 + 1 + 1 MILC highly-improved staggered quark (HISQ) ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited state systematics with the new method and obtain value of gA = 1.213(26) with a quark-mass dependent renormalization coefficient.

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin SG in the Coulomb gauge in the MS scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of SG in the range 0 ≤ | p| < 1.5 GeV is very mild, and we determine it in the large momentum limit to be SG = 0.251(47)(16) at the physical pion mass in the MS scheme at µ 2 = 10 GeV 2. If the matching procedure in large momentum effective theory is neglected, SG is equal to the glue helicity measured in high-energy scattering experiments.

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin SG in the Coulomb gauge in the MS scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of SG in the range 0 ≤ | p| < 1.5 GeV is very mild, and we determine it in the large momentum limit to be SG = 0.251(47)(16) at the physical pion mass in the MS scheme at µ 2 = 10 GeV 2. If the matching procedure in large momentum effective theory is neglected, SG is equal to the glue helicity measured in high-energy scattering experiments.

We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling g 3 A with overlap valence on 2 + 1-flavor domain wall fermion (DWF) sea. Using the equality of g 3 A from the spatial and temporal components of the axialvector current as a normalization condition, we find that g 3 A is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges g 3 A (24I) = 1.22(4)(3) and g 3 A (32I) = 1.21(3)(3) are obtained on a 24 3 × 64 lattice at pion mass of 330 MeV and a 32 3 × 64 lattice at pion mass 300 MeV and are increased by 3.4% and 1.7% from their unimproved values, respectively. We have also used clover fermions on the same DWF configurations and find the same behavior for the local axial charge as that with overlap fermions.

We pursue further an approach to lattice chiral fermions in which the fermions are treated in the continuum. To render the effective action gauge invariant, counterterms have to be introduced. We determine the counterterms for smooth gauge fields, both analytically and numerically. The final result is that the imaginary part of the effective action can be computed analytically from the lattice gauge field, while the real part is given by one half of the action of the corresponding vector model.

The axial charge of the nucleon g A and the pion decay constant f π are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as m π = 130 MeV. Both quantities, g A and f π , suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio g A /f π , we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find g R A = 1.29(5)(3), using the physical value of f π as input and r 0 = 0.50(1) to set the scale. In a subsequent calculation we attempt to extrapolate g A and f π separately to the infinite volume. Both volume and quark mass dependencies of g A and f π are found to be well decribed by ChEFT and ChPT. We find at the physical point g R A = 1.24(4) and f R π = 89.6(1.1)(1.8) MeV. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constantl 4 = 4.2(1).

We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to extract quantities like Polyakov loop correlators, effective Polyakov loop potentials and baryon density.

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).

We have performed numerical simulations of SU(3) gauge theory coupled to N f = 2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L = 6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.

1. overlap fermions and their numerical implementation 2. overlap fermions on T=0 quenched Lüscher-Weisz gauge-field configurations and Random Matrix Theory 3. valence overlap fermions on dynamical Wilson-Clover configurations in the vicinity of the chiral phase transition Forschergruppen-Treffen, Regensburg, 21.12.2004 1 Overlap Fermions and their Numerical Implementation Wilson Fermions • Wilson term − r 2 P nΨ (n)2Ψ(n) added to naive discretization of fermionic action to avoid doublers • chiral symmetry explicitly broken γ 5 D + Dγ 5 = 0 • improvement necessary to achieve O(a) • additive renormalization of quark mass necessary • no satisfactory definition of topological charge • plagued by the appearance of exceptional configurations • numerically not so expensive • local Forschergruppen-Treffen, Regensburg, 21.12.2004 The Overlap Operator • exact chiral symmetry on the lattice • index theorem → allows investigation of the relation between topological properties of gauge fields and the dynamics of chiral fermions • no O(a) improvement necessary • no exceptional configurations → simulation at small quark masses allows us to make contact with (quenched) chiral perturbation theory • numerically very expensive • only local in generalized sense • additional irrelevant parameter ρ Forschergruppen-Treffen, Regensburg, 21.12.2004

We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The efficacy of the algorithm is tested in Monte Carlo simulations of Wilson quarks in quenched QCD. Applications that are difficult to probe with point propagators are discussed.

In a full QCD lattice study with N f = 2 Wilson fermions, we seek to optimize the signals for the disconnected contributions to the matrix element of flavoursinglet operators between nucleon states, which are indicative for sea quark effects. We demonstrate, in form of a fluctuation analysis to the noisy estimator technique, that -in order to achieve a tolerable signal to noise-ratio in full QCD -it is advantageous to work with a Z 2 -noise source rather than to rely only on gauge invariance to cancel non-gauge-invariant background. In the case of the πN σ-term, we find that 10 Z 2 -noise sources suffice on our sample ( about 150 independent QCD configurations at β = 5.6 on 16 3 × 32 with κ sea = 0.157, equivalent to M π /M ρ = 0.76(1)), to achieve decent signals and adequate fluctuations, rather than 300 such sources as recently used in quenched simulations.

A study has been performed of the reaction pp → 4K ± using in-flight antiprotons from 1.1 to 2.0 GeV/c incident momentum interacting with a hydrogen jet target. The reaction is dominated by the production of a pair of φ mesons. Thepp → φφ cross section rises sharply above threshold and then falls continuously as a function of increasing antiproton momentum. The overall magnitude of the cross section exceeds expectations from a simple application of the OZI rule by two orders of magnitude. In a fine scan around the ξ/fJ (2230) resonance, no structure is observed. A limit is set for the double branching ratio B(ξ → pp) × B(ξ → φφ) < 6 × 10 −5 for a spin 2 resonance of M = 2.235 GeV and Γ = 15 MeV.

The contribution of quarks to the effective potential for the phase of the Wilson line is computed at nonzero temperature and quark chemical potential to one and two loop order. At zero temperature, regardless of the value of the quark chemical potential, the effective potential for the phase of the Wilson line vanishes. At nonzero temperature, for special values of the phase the free energy of quarks equals that of bosons; at nonzero chemical potential, such quarks can ``Bose condense'', albeit with negative density.

We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with $Z_4$ noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a $16^3 \times 24$ quenched lattice at $\beta = 6.0$ for Wilson fermions with $\kappa=0.154, 0.155$, and $0.1555$ which correspond to pion masses at $650, 538$, and $478$ MeV, respectively. The chirally extrapolated $u$ and $d$ quark momentum/angular momentum fraction is found to be $0.64(5)/0.70(5)$, the strange momentum/angular momentum fraction is $0.023(6)/0.022(7)$, and that of the glue is $0.33(6)/0.28(8)$. The previous study of quark spin on the same lattice revealed that it carries a fraction of $0.25(12)$ of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes $0.47(13)$ of the proton spin with almost all of it coming from the disconnected insertions.

We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.

We study the strangeness electromagnetic form factors of the nucleon from the N f = 2 + 1 clover fermion lattice QCD calculation. The disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. In addition to increasing the number of Z(4) noises, we find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G s M (0) = −0.017 , where the first error is statistical, and the second is the uncertainties in Q 2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error. We also study the strangeness second moment of the partion distribution function of the nucleon, x 2 s−s .

The calculation of the nucleon strangeness form factors from N_f=2+1 clover fermion lattice QCD is presented. Disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), which is consistent with experimental values, and has an order of magnitude smaller error. Preliminary results for the strangeness contribution to the second moment of the parton distribution function are also presented.

The calculation of the nucleon strangeness form factors from N f = 2 + 1 clover fermion lattice QCD is presented. Disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G s M (0) = −0.017 , which is consistent with experimental values, and has an order of magnitude smaller error. Preliminary results for the strangeness contribution to the second moment of the parton distribution function are also presented. PACS: 13.40.-f, 12.38.Gc, 14.20.Dh

We study the strangeness contribution to nucleon matrix elements using N f = 2 + 1 dynamical clover fermion configurations generated by the CP-PACS/JLQCD collaboration. In order to evaluate the disconnected insertion (DI), we use the Z(4) stochastic method, along with unbiased subtraction from the hopping parameter expansion which reduces the off-diagonal noises in the stochastic method. Furthermore, we find that using many nucleon sources for each configuration is effective in improving the signal. Our results for the quark contribution to the first moment x q in the DI, and the strangeness magnetic moment show that the statistical errors are under control with these techniques. We also study the gluonic contribution to the nucleon using the overlap operator to construct the gauge field tensor, F µν . The application to the calculation of first moment, x G , gives a good signal in quenched lattice QCD.

We study the meta-stable states in high temperature phase of QCD characterised by nonzero expectation values for the imaginary part of the Polyakov loop. We consider $N_f= 2, 3$ dynamical staggered quarks, and carry out simulations at various values of the coupling $\beta$ to observe these states. In particular, we find the value of the coupling ($\beta_m$) above which the meta-stable states appear. The resulting value of $\beta_m$ corresponds to temperature $T_m \gtrsim 750$MeV for $N_f=2$.

The second Nachtmann moment of the I-spin = 2 linear combination of pion structure function, which is a pure higher-twist effect, is calculated in lattice QCD at β = 6.0 with Wilson fermions in the quenched approximation. The values of B-factors of the spin-2 four-fermions operators involved in the calculation span between 0.5 and 2.0, so that the higher-twist scale for this particular moment turns out to be of the order of the pion decay constant. The results of lattice calculation are compared with the ones from the bag model, the potential quark models and the 1/N approximation.