Lattice perturbation theory

The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of computations on the lattice, especially for investigating the behavior of lattice theories near the continuum limit. Particularly important is its role in connecting the outcome of Monte Carlo simulations to continuum physical results. For these matchings the calculation of the renormalization factors of lattice matrix elements is required. In this review we explain the main methods and techniques of lattice perturbation theory, focusing on the cases of Wilson and Ginsparg-Wilson fermions. We illustrate, among other topics, the peculiarities of perturbative techniques on the lattice, the use of computer codes for the analytic calculations and the computation of lattice integrals. Discussed are also methods for the computation of 1-loop integrals with very high precision. The review presents in a pedagogical fashion also some of the recent developments in this kind of calculations. The coordinate method of Luescher and Weisz is explained in detail. Also discussed are the novelties that Ginsparg-Wilson fermions have brought from the point of view of perturbation theory. Particular emphasis is given throughout the paper to the role of chiral symmetry on the lattice and to the mixing of lattice operators under renormalization. The construction of chiral gauge theories regularized on the lattice, made possible by the recent advances in the understanding of chiral symmetry, is also discussed. Finally, a few detailed examples of lattice perturbative calculations are presented. (orig.)Available from TIB Hannover: RA 2999(02-185) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Status of lattice structure function calculations

The moments of structure functions can be calculated from first principles, without making any model assumptions, using the non-perturbative techniques of lattice QCD. Numerous results have been obtained from lattice computations in the last years. They include the calculation of the lowest moments of the unpolarized structure functions, of the spin-dependent g_1 and g_2 structure functions and of the h_1 transversity structure function. Some higher-twist matrix elements have been studied as well. The novelties of the last couple of years are the first computations of structure functions done in full QCD (unquenched), and new proposals for the extrapolations to the chiral limit using chiral perturbation theory. A lot of work however still needs to be done in order to control other systematic uncertainties like the continuum limit or the non-perturbative renormalization. (orig.)Available from TIB Hannover: RA 2999(02-067) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the #LAMBDA#-parameter of the theory is obtained with a total error of 8%. (orig.)73 refs.Available from TIB Hannover: RA 2999(98-154) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Study of lattice correlation functions at small times using the QCD sum rules continuum model

In this paper we study the work of Leinweber by applying the continuum model of QCD sum rules (QCDSR) to the analysis of (quenched) lattice correlation functions. We expand upon his work in several areas: we study meson states as well as baryons; we analyse data from several lattice spacings; and we include data from the Sheikholeslami-Wohlert (clover) improved action. We find that the QCDSR continuum model ansatz can reproduce the data, but only for non-physical values of its parameters. This leads us to reject it as a model for hadronic correlation functions. We study the non-relativistic quark model and conclude that it predicts essentially the same form for the correlation function as the QCDSR continuum model approach. Furthermore, because it doesn't have the continuum model's restrictions on the parameters, the non-relativistic quark model can be viewed as a successful Ansatz. As well as studying the validity or otherwise of the QCDSR continuum model approach, this paper defines 4-parameter fitting functions that can be used to fit lattice data even for a time window close to the source. These functions are shown to be an improvement over 2-exponential fits especially in the case of mesons. We encourage the application of this approach to situations where the conventional fitting procedures are problematic due to poor ground state dominance. (orig.)Available from TIB Hannover: RA 2999(97-185) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Towards a non-perturbative calculation of DIS Wilson coefficients

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. (orig.)Available from TIB Hannover: RA 2999(98-147) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Perturbative renormalization of improved lattice operators

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). (orig.)SIGLEAvailable from TIB Hannover: RA 2999(97-181) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Local bilinear operators on the lattice and their perturbative renormalisation including O(#alpha#) effects

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. (orig.)Talk given by Schiller, A., 2nd SPIN Workshop, Zeuthen (DE), September 1-5, 1997Available from TIB Hannover: RA 2999(97-216) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Non-perturbative improvement and renormalization of lattice operators

The Alpha Collaboration has proposed an optimal value for c_s_w 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 identitiesSIGLEAvailable from TIB Hannover: RA 2999(97-180) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

O(a) improvement of nucleon matrix elements

We report on preliminary results of a high statistics quenched lattice QCD calculation of nucleon matrix elements within the Symanzik improvement programme. Using the recently determined renormalisation constants from the alpha collaboration we present a fully non-pertubative calculation of the forward nucleon axial matrix element with O(a) lattice artifacts completely removed. Runs are made at #beta# = 6.0 and #beta# = 6.2, in an attempt to check scaling and O(a"2) effects. We shall also briefly describe results for left angle x right angle, the matrix element of a higher derivative operator. (orig.)SIGLEAvailable from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Higher-twist corrections to nucleon structure functions from lattice QCD

A genuinely non-perturbative evaluation of higher-twist contributions to the structure functions of the nucleon, with all mixing effects and renormalon ambiguities taken care of, is presented. Higher-twist corrections turn out to be significant at moderate values of q"2. (orig.)6 refs.Available from TIB Hannover: RA 2999(99-069) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman