W. Detmold

Analytic properties of the Landau gauge gluon and quark propagators

We explore the analytic structure of the gluon and quark propagators of Landau gauge QCD from numerical solutions of the coupled system of renormalized Dyson-Schwinger equations and from fits to lattice data. We find sizable negative norm contributions in the transverse gluon propagator indicating the absence of the transverse gluon from the physical spectrum. A simple analytic structure for the gluon propagator is proposed. For the quark propagator we find evidence for a masslike singularity on the real timelike momentum axis, with a mass of 350 to 500 MeV. Within the Greens function approach that is employed, we identify a crucial term in the quark-gluon vertex that leads to a positive definite Schwinger function for the quark propagator.

Moments of isovector quark distributions in lattice QCD

We present a complete analysis of the chiral extrapolation of lattice moments of all twist-2 isovector quark distributions, including corrections from N pi and Delta pi loops. Even though the Delta resonance formally gives rise to higher order non-analytic structure, the coefficients of the higher order terms for the helicity and transversity moments are large and cancel much of the curvature generated by the wave function renormalization. The net effect is that, whereas the unpolarized moments exhibit considerable curvature, the polarized moments show little deviation from linearity as the chiral limit is approached.

Analytic structure of the gluon and quark propagators in Landau gauge QCD

In Landau gauge QCD, the infrared behavior of the propagator of transverse gluons can be analytically determined to be a power law from Dyson–Schwinger equations. This propagator clearly shows positivity violation, indicating the absence of the transverse gluons from the physical spectrum, i.e. gluon confinement. A simple analytic structure for the gluon propagator is proposed capturing all important features. We provide arguments that the Landau gauge quark propagator possesses a singularity on the real timelike axis. For this propagator we find a positive definite Schwinger function.

Electromagnetic and spin polarizabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarizabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarizabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of finite volume chiral perturbation theory. We derive results relevant for lattice simulations of QCD, partially-quenched QCD and quenched QCD. Our results for the polarizabilities show a strong dependence on the lattice volume and quark masses, typically differing from the infinite volume limit by {approx}10% for current lattice volumes and quark masses.

Flavor singlet physics in lattice QCD with background fields

We show that hadronic matrix elements can be extracted from lattice simulations with background fields that arise from operator exponentiation. Importantly, flavor-singlet matrix elements can be evaluated without requiring the computation of disconnected diagrams, thus facilitating a calculation of the quark contribution to the spin of the proton and the singlet axial coupling, g{sub A}{sup 0}. In the two-nucleon sector, a background field approach will allow calculation of the magnetic and quadrupole moments of the deuteron and an investigation of the EMC effect directly from lattice QCD. Matrix elements between states of differing momenta are also analyzed in the presence of background fields.

Double distributions for the proton

We derive double distributions for the proton in a simple model that contains scalar as well as axial-vector diquark correlations. The model parameters are tuned so that the experimentally measured electromagnetic form factors of the proton are reproduced for small momentum transfer. Resulting generalized parton distributions satisfy known constraints, including the positivity bounds.

Extraction of parton distributions from lattice QCD

We review the calculation of moments of both the polarized and unpolarized parton distribution functions of the nucleon in lattice QCD, and in particular their extrapolation to the physical region. We also discuss the reconstruction of the x dependence of the valence quark distributions in the nucleon from a finite number of lattice moments.

Role of the nuclear vector potential in deep inelastic scattering

We study the influence of the strong nuclear vector potential, treated using the mean-field approximation, in deep inelastic scattering. A physically consistent treatment of the electromagnetic current operator, combined with the use of the operator product expansion is presented and discussed.

Complex conjugate poles and parton distributions

We calculate parton and generalized parton distributions in Minkowski space using a scalar propagator with a pair of complex conjugate poles. Correct spectral and support properties are obtained only after careful analytic continuation from Euclidean space. Alternately the quark distribution function can be calculated from modified cutting rules, which put the intermediate state on its complex mass shells. Distribution functions agree with those resulting from the models Euclidean space double distribution which we calculate via non-diagonal matrix elements of twist-two operators. Thus one can use a wide class of analytic parameterizations of the quark propagator to connect Euclidean space Green functions to light-cone dominated amplitudes.

Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model

In a scalar