arXiv subjects
Publications and source records attributed to M. Goeckeler.
The renormalisation constants for local bilinear quark operators are calculated using the Sheikholeslami-Wohlert improved action. In addition we compute the renormalisation constant of the leading gluon operator for different group representations and discuss the mixing of the operators E^2 and B^2.
About half the mass of a hadron is given from gluonic contributions. In this talk we calculate the chromo-electric and chromo-magnetic components of the nucleon mass. These computations are numerically difficult due to gluon field ultra-violet fluctuations. Nevertheless a high statistics feasibility run using quenched Wilson fermions seems to show reasonable signals.
For lattice operators that are relevant to the calculation of moments of nucleon structure functions we investigate the transformation properties under the hypercubic group. We give explicit bases of irreducible subspaces for tensors of rank up to 4.
We review our progress on the lattice calculation of low moments of both the unpolarised and polarised nucleon structure functions.
We describe a high statistics quenched QCD calculation of the moments of the polarized deep-inelastic structure functions g_1 and g_2 of the proton and neutron.
We extract scattering phases for fermion-fermion scattering from Monte Carlo simulations of the two-dimensional Gross-Neveu model. This is done by means of Lüscher's method, which exploits the volume dependence of the energies of two-particle states. The results are compared with the analytical predictions.
We investigate effective Yukawa couplings of mesons to the elementary fermions in noncompact lattice QED. The couplings are extracted from suitable fermion-antifermion-meson three-point functions calculated by Monte Carlo simulations with dynamical staggered fermions. The scaling behaviour is compatible with expectations from perturbation theory, thus indicating triviality of QED. The lines of constant Yukawa coupling are compared to flows of other quantities. Consistency is seen, at most, for weak coupling.
We have initiated a programme to compute the lower moments of the unpolarised and polarised deep inelastic structure functions of the nucleon in the quenched approximation. We review our progress to date.
We present new Monte Carlo results in non-compact lattice QED with staggered fermions down to m_0 = 0.005. This extends our previous investigations on the nature of the continuum limit of QED.
According to a proposal of Luescher it is possible to determine elastic scattering phases in infinite volume from the energy spectrum of two-particle states in a periodic box. We demonstrate the applicability of this method in the broken phase of the four-dimensional O(4) non-linear sigma-model in a Monte Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the sigma-particle in our case. We observe the sigma-resonance and extract its mass and width. In all scattering channels investigated the results are completely consistent with perturbative calculations.
We investigate a lattice Nambu--Jona-Lasinio model both by the Monte Carlo method and Schwinger-Dyson equations. A comparison allows the discussion of finite size effects and the extrapolation to infinite volume. We pay special attention to the identification of particles and resonances. This enables us to discuss renormalisation group flows in the neighbourhood of the critical coupling where the chiral symmetry breaking phase transition takes place. In no region of the bare parameter space do we find renormalisability for the model.
We investigate the neighbourhood of the chiral phase transition in a lattice Nambu--Jona-Lasinio model, using both Monte Carlo methods and lattice Schwinger-Dyson equations.
We report on calculations of the hadronic coupling constants $g_{ρππ}$ and $g_{nnπ}$ based on lattice QCD with four flavors of dynamical staggered fermions. By computing 2--point and 3--point Green's functions we have been able to determine these coupling constants ab initio from QCD; the results are compatible with the experimental values.
We give a 1993 update of non-compact lattice QED, in particular the chiral condensate, finite size effects and meson mass ratios. We compare descriptions of the phase transition. Our previous conclusions remain valid.
Using Luescher's method we determine the elastic scattering phases in the broken phase of the 4-dimensional O(4) non-linear sigma-model from the two-particle energy spectrum in a Monte-Carlo study on finite lattices. In the isospin-0-channel we observe the sigma-resonance and extract its mass and its width. In all scattering channels investigated the results are consistent with perturbative calculations.
We calculate fermion-antifermion-"meson" three-point functions in noncompact lattice QED with dynamical staggered fermions and use them to extract effective Yukawa couplings. The results are consistent with the hypothesis that QED is trivial.
A lattice calculation of the pi-N sigma term is described using dynamical staggered fermions. Preliminary results give a sea term comparable in magnitude to the valence term.
We will discuss here an indirect lattice evaluation of the baryon axial singlet current matrix element. This quantity may be related to the fraction of nucleon spin carried by the quarks. The appropriate structure function has recently been measured (EMC experiment). As in this experiment, we find that the quarks do not appear to carry a large component of the nucleon spin.