Fundamental parameters of QCD

The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant #alpha#_s and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of #alpha#_s and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required. (orig.)Available from TIB Hannover: RA 2999(02-030) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Non-perturbative renormalization of HQET and QCD

We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off-shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the heavy quark effective theory (HQET). (orig.)SIGLEAvailable from TIB Hannover: RA 2999(02-132) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Beauty physics in lattice gauge theory

We summarize the present status of lattice gauge theory computations of the leptonic decay constants f_D and f_B. The various sources of systematic errors are explained in a manner easily understood by the non-expert. The results obtained by the different groups are then systematically compared. As a result, we derive estimates for f_D and f_B in the quenched approximation through an appropriate combination of the data available from the different groups. Since we account for a possible lattice spacing dependence, the final errors are quite large. However, it is now well known how these uncertainties can be reduced. For the decay constant of heavy-light pseudoscalar mesons with masses of 1-2 GeV, an interesting comparison of a full QCD result with the corresponding simulation in the quenched approximation can be done. Effects of sea quarks of mass m_s are below the statistical accuracy of these simulations. Related quantities, like B-parameters, the spectrum of beauty-hadrons and the breaking of the QCD string are discussed briefly. (orig.)Available from TIB Hannover: RA 2999(94-011) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Renormalization and O(#alpha#)-improvement of the static axial current

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schroedinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC-simulations. We evaluate its lattice spacing effects in perturbation theory. (orig.)Available from TIB Hannover: RA 2999(00-091) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Renormalization of the static-light axial current

We discuss the determination of the heavy-light axial current renormalization in the static approximation, using a new method based on the Schroedinger functional (SF). Previous perturbative results for the renormalization constant are confirmed. (orig.)Available from TIB Hannover: RA 2999(99-145) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A new way to set the energy scale in lattice gauge theories and its applications to the static force and #alpha#_s in SU(2) Yang-Mills theory

We introduce a hadronic scale R_0 through the force F(r) between static quarks at intermediate distances r. The definition F(R_0)R_0"2 = 1.65 amounts to R_0 #approx =# 0.5 fm in phenomenological potential models. Since R_0 is well defined and can be calculated accurately in a Monte Carlo simulation, it is an ideal quantity to set the scale. In SU(2) pure gauge theory, we use new data (and R_0 to set the scale) to extrapolate F(r) to the continuum limit for distances r = 0.18 fm to r = 1.1 fm. Through R_0 we determine the energy scale in the recently calculated running coupling constant, which used the recursive finite size technique to reach large energy scales. Also in this case, the lattice data can be extrapolated to the continuum limit. The use of one loop Symanzik improvement is seen to reduce the lattice spacing dependence significantly. (orig.)Available from TIB Hannover: RA 2999(93-062) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The N_f=0 heavy quark potential from short to intermediate distances

We study the potential of a static quark anti-quark pair in the range 0.05 fm#<=#r#<=#0.8fm, employing a sequence of lattices up to 64"4. Lattice artifacts in potential and force are investigated theoretically as well as numerically and continuum quantities are obtained by extrapolation of the results at finite lattice spacing. Consistency of the numerical results with the form of scaling violations predicted by an analysis a la Symanzik is found. The scale r_0/a is determined for the Wilson action up to #beta#=6.92. (orig.)Available from TIB Hannover: RA 2999(01-095) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Non-perturbative renormalization of QCD

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schroedinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the #LAMBDA#-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement. (orig.)Available from TIB Hannover: RA 2999(97-207) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The #LAMBDA#-parameter and m_s of quenched QCD

We explain how scale dependent renormalized quantities can be computed using lattice QCD. Two examples are used: the running coupling and quark masses. A reliable computation of the #LAMBDA#-parameter in the quenched approximation is presented. (orig.)9 refs.Available from TIB Hannover: RA 2999(97-223) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

String breaking in SU(2) gauge theory with scalar matter fields

We investigate the static potential in the confinement phase of the SU(2) Higgs model on the lattice, where this model is expected to have properties similar to QCD. We observe that Wilson loops are inadequate to determine the potential at large distances, where the formation of two color-neutral mesons is expected. Introducing smeared fields and a suitable matrix correlation function, we are able to overcome this difficulty. We observe string breaking at a distance r_b#approx#1.8 r_0, where the length scale r_0 has a value r_0#approx#0.5 fm in QCD. The method presented here may lead the way towards a treatment of string breaking in QCD. (orig.)Available from TIB Hannover: RA 2999(98-088) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman