arXiv subjects
Publications and source records attributed to G. Schierholz.
The evaluation of the higher twist contributions to Deep Inelastic Scattering amplitudes involves a non trivial choice of operator bases for the higher orders of the OPE expansion of the two hadronic currents. In this talk we discuss the perturbative renormalization of the four-fermion operators that appear in the above bases.
We verify the operator product expansion (OPE) of deep inelastic scattering (DIS) on the lattice and present first results of a non-perturbative calculation of the Wilson coefficients.
Nucleon form factors have been extensively studied both experimentally and theoretically for many years. We report here on new results of a high statistics quenched lattice QCD calculation of vector and axial-vector nucleon form factors at low momentum transfer within the Symanzik improvement programme. The simulations are performed at three kappa and three beta values allowing first an extrapolation to the chiral limit and then an extrapolation in the lattice spacing to the continuum limit. The computations are all fully non-perturbative. A comparison with experimental results is made.
Quenched lattice QCD calculations with Wilson-type fermions at small quark masses are impeded by exceptional configurations. We show how this problem can be resolved in a practicable way without changing the physics in the chiral limit.
We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
We investigate the nonperturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
A recently proposed method for regularizing chiral gauge theories non-perturbatively is discussed in detail. The result is an effective action which can be computed from the lattice gauge field, and which is suited for numerical simulations.
We discuss a method for regularizing chiral gauge theories. The idea is to formulate the gauge fields on the lattice, while the fermion determinant is regularized and computed in the continuum. A simple effective action emerges which lends itself to numerical simulations.
We briefly describe some of our recent results for the mass spectrum and matrix elements using $O(a)$ improved fermions for quenched QCD. Where possible a comparison is made between improved and Wilson fermions.
We present new numerical results for the renormalized mass and coupling in non-compact lattice QED with staggered fermions. Implications for the continuum limit and the role of the Landau pole are discussed.
We investigate a lattice version of QED by numerical simulations. For the renormalized charge and mass we find results which are consistent with the renormalized charge vanishing in the continuum limit. A detailed study of the relation between bare and renormalized quantities reveals that the Landau pole lies in a region of parameter space which is made inaccessible by spontaneous chiral symmetry breaking.
We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary coefficients of the improvement terms. We have thus control over O(a) corrections, and for a suitable choice of improvement coefficients we are only left with errors of O(a^2).
Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These $Z$ factors can be used to relate matrix elements measured by lattice techniques to their continuum counterparts. We discuss the $O(a)$ improvement of point and one-link lattice quark operators. Suitable bases of improved operators are derived. Tadpole improvement is applied to get more reliable perturbative results.
We report on new results of the spin dependent structure functions $g_1$ and $h_1$ of the nucleon. An attempt is made to convert the moments, which is what one computes on the lattice, to quark distribution functions.
We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16^3x32 lattices at beta = 6.0 for 3 kappa values in each case. The improved sources greatly decrease the statistical noise. We extract and discuss here renormalization factors for local operators and moments of the structure functions for Wilson fermions.
We compute the lower moments of the structure functions of $π$ and $ρ$. Of particular interest are the spin-dependent structure functions of the $ρ$ as they give new information about quark binding effects.
We have results from light hadron simulations in quenched QCD at beta=6.0 and 6.2 using non-perturbatively improved Sheikholeslami-Wohlert fermions in an effort to remove all order(a) effects. From looking at hadron masses and splittings and the RG-invariant quark masses (where we have one point at beta=5.7) we suggest this is plausible even with the limited data set. The interpretation of the decay constants appears to be less clear.
The Alpha Collaboration has proposed an optimal value for c_SW in the Sheikholeslami-Wohlert action, chosen to remove O(a) effects. To measure hadronic matrix elements to the same accuracy we need a method of finding O(a) improved operators, and their renormalization constants. We determine the Z factors by a non-perturbative method, measuring the matrix elements for single quark states propagating through gauge fields in the Landau gauge. The data show large effects coming from chiral symmetry breaking. This allows us to find the improvement coefficients too, by requiring that the amount of chiral symmetry breaking agrees with that predicted by the chiral Ward identities.