M. Göckeler

Polarized and unpolarized nucleon structure functions from lattice QCD

We report on a high statistics quenched lattice QCD calculation of the deep-inelastic structure functions {ital F}{sub 1}, {ital F}{sub 2}, {ital g}{sub 1}, and {ital g}{sub 2} of the proton and neutron. The theoretical basis for the calculation is the operator product expansion. We consider the moments of the leading twist operators up to spin four. Using Wilson fermions the calculation is done for three values of {kappa}, and we perform the extrapolation to the chiral limit. The renormalization constants, which lead us from lattice to continuum operators, are calculated in perturbation theory to one loop order. {copyright} {ital 1996 The American Physical Society.}

Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks

QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2+1 flavour case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

Abstract 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 .

Renormalisation and off-shell improvement in lattice perturbation theory

Abstract We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami–Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m 2 /p 2 , in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg–Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.

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.

Nucleon electromagnetic form factors on the lattice and in chiral effective field theory

We compute the electromagnetic form factors of the nucleon in quenched lattice QCD, using nonperturbatively improved Wilson fermions, and compare the results with phenomenology and chiral effective field theory.

Scaling of nonperturbatively O ( a ) -improved Wilson fermions: Hadron spectrum, quark masses, and decay constants

We compute the hadron mass spectrum, the quark masses, and the meson decay constants in quenched lattice QCD with nonperturbatively

Strangeness Contribution to the Proton Spin from Lattice QCD

O(a)

The pion form factor from lattice QCD with two dynamical flavours

-improved Wilson fermions. The calculations are done for two values of the coupling constant

Determination of light and strange quark masses from two-flavour dynamical lattice QCD

\ensuremath{\beta}=6.0