We analyze N f = 2 nucleon mass data with respect to their dependence on the pion mass down to m π = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon σ-term. Our lattice data below m π = 435 MeV is well described by O(p 4 ) BChPT and we find σ = 37(8)(6) MeV for the σ-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r 0 = 0.501(10)(11) fm.

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 Z4 noise, and the signal-to-noise ratio 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 163 x 24 quenched lattice at f) = 6.0 for Wilson fermions with k = 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. L INTRODUCTIOND eterm ining the contributions from quarks and gluons to the nucleon spin is one o f the m ost challenging issues in QCD both experim entally and theoretically. Since the contribution from the quark spin is found out to be small (~25% o f the total proton spin) from the global analysis of deep inelastic scattering data [1], it is expected that the rest should com e from glue spin and the orbital angular m om enta o f quarks and glue.The quark spin contribution from u, d, and s has been studied on the lattice [2,3] since 1995 using either the quenched approxim ation or dynam ical ferm ions with heavier quark m ass [4], Recently, it has been carried out with light dynam ical ferm ions [5,6] and only for strange quarks (not renorm alized) in Ref. [7]. The calculation of disconnected insertion (DI) contributions to quark spin *mpdeka@theor.jinr.ru Vbyang@pa.uky.edu 'liu@pa.uky.edu from u, d, s, and c using the anom alous W ard identity with light overlap ferm ions is under progress [8].As for the quark orbital angular mom enta, lattice calcu lations have been carried out for the connected insertions (Cl) [9-15], They are obtained by subtracting the quark spin contributions from those o f the quark angular mom enta. It has been show n that the contributions from u and d quarks m ostly cancel each other. Thus, for connected insertion, quark orbital angular m om enta turn out to be small in the quenched calculation [9,10] and nearly zero in dynamical fermion calculations [11][12][13][14][15]. On the other hand, gluon helicity distribution A G (x) /G ( jc) from COM PASS, STAR, HERM ES, and PHENIX experim ents is found to be close to zero [16][17][18][19][20]. The latest global fit [21] with the inclusion of the polarized deep inelastic scattering (DIS) data from COMPASS [22] and the ...

We extend the study of lowest moments, x and x 2 , of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a 16 3 × 24 quenched lattice with Wilson fermion. The quark loops are calculated with Z 2 noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5σ signals for x for the u, d, and s quarks, but x 2 is consistent with zero within errors.We provide results for both the connected and disconnected insertions. The perturbatively renormalizedx for the strange quark at µ = 2 GeV is x s+s = 0.027 ± 0.006 which is consistent with the experimental result. The ratio of x for s vs. u/d in the disconnected insertion with quark loops is calculated to be 0.88 ± 0.07. This is about twice as large as the phenomenologically fitted x s+s x ū + x d from experiments whereū andd include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.

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We determine the second Mellin moment of the isovector quark parton distribution function x u−d from lattice QCD with N f = 2 sea quark flavours, employing the non-perturbatively improved Wilson-Sheikholeslami-Wohlert action at a pseudoscalar mass mπ = 157(6) MeV. The result is converted non-perturbatively to the RI'-MOM scheme and then perturbatively to the MS scheme at a scale µ = 2 GeV. As the quark mass is reduced we find the lattice prediction to approach the value extracted from experiments. PACS numbers: 12.38.Gc,14.20.Dh Almost all visible matter is composed of protons and neutrons. Analyses of the scattering of cosmic ray particles off nuclei or of results from fixed target and colliding hadron beam experiments require a quantitative understanding of the partonic structure of nucleons. The theoretical framework for this is known [1, 2] since the inception of quantum chromodynamics (QCD); see also [3,4].Of particular importance for the experimental programmes at the Large Hadron Collider are unpolarized parton distribution functions (PDFs). These, in the lightcone frame, parameterize the likelihood of a parton to carry the Bjorken momentum fraction x at a renormalization scale µ. While these PDFs have been mapped out very well from fits to experimental data, ideally one would wish to evaluate them directly from the underlying fundamental theory, QCD.The present method of choice is lattice QCD, where in principle all approximations can be removed and systematic uncertainties controlled by taking the limits of infinite volume, of vanishing lattice spacing (a → 0) and of physical quark masses. However, in this Monte Carlo simulation approach to QCD, the statistical errors and the reliability of the extrapolation to the physical point are limited by the power of available computers and the efficiency of numerical algorithms. Moreover, only Mellin moments of the PDFs can be accessed. Thus, present-day lattice simulation cannot compete in terms of precision with determinations of isovector unpolarized PDFs from fits to experimental photon-nucleon scattering data that have been collected over decades of dedicated effort. For a summary of the present status of PDF parametrizations, see [5].The possibility to predict averages over the momentum fraction, however, is complementary to experimental measurements that can only cover a limited range of x values. In particular, the strangeness and gluonic PDFs are determined rather indirectly from experiment, with large uncertainties [6]. Consequently, lattice QCD is already on the verge of becoming essential to constrain these and other less well known quantities, e.g., the pion nucleon σ term [7][8][9][10][11], the strangeness fraction of the mass of the proton f Ts [8][9][10][11][12][13], the strange quark contribution to the spin of the proton ∆s + ∆s [13,14] or individual (valence and sea) quark contributions to the proton's momentum x u , x d and x s [15]. Naturally, for lattice predictions of such quantities to be trusted, lattice QCD needs to demonstrate its ab...