Werner Wetzel

Electro-weak radiative corrections for e+e− → μ+μ− at LEP energies

Abstract We present a calculation of the radiative correctons to e + e − → μ + μ − within the standard model for the weak and electromagnetic interactions. The center-of-mass energies considered range from 40 to 150 GeV. The integrated cross section and the forward-backward asymmetry are discussed in detail. We find for the former that QED bremsstrahlung constitutes by far the largest fraction of the radiative corrections. For the asymmetry however the radiative corrections other than QED bremsstrahlung are equally important and even dominate at energies close to the Z-pole.

On the Quark Mass Dependence of the Parameters of Quantum Chromodynamics

Abstract The running coupling constant and quark masses in QCD are calculated in the one-loop approximation using the 3-gluon vertex to define the coupling constant. Our results differ for finite quark masses from those reported previously in the literature. We discuss the origin of this apparent discrepancy. We also make some comments on the gauge dependence of the QCD parameters.

EXTENDING IMPROVEMENT TO FERMIONS

Abstract Tree-level improvement of the lattice action for SU(N) gauge theory is extended to Wilson fermions. The cancellation of lattice artefacts is verified for quark-quark and quark-gluon scattering to ordrder a2 in the lattice spacing a.

The relation between the Λ parameters of the standard and of the continuum limit improved lattice action for pure Yang-Mills theory

Abstract The relation between the scale parameter Λ W of the Wilson action and the corresponding scale Λ I of the continuum limit improved action for SU( N ) lattice gauge theory is calculated. We find that Λ I / Λ W = 4.13 ± 0.01 for N = 2 and Λ I / Λ W = 5.29 ± 0.01 for N = 3.

Symanzik's improvement program applied to the Gross-Neveu model at large N

Abstract Symanziks improvement program for lattice actions is applied to the large- N limit of the Gross-Neveu model in the σ-field formulation. We construct a series of actions which suppress scaling violations up to order a 2 at tree level, the l-loop level, and to all orders in the large- N coupling λ = g 2 N . The fermions are treated by Wilsons method. We investigate the gap equation for the dynamical fermion mass. For this nonperturbative quantity it is shown that the correlation between the order of improvement and the order to which powers of ln a are supressed follows the pattern expected from perturbation theory, i.e. tree improvement removes the leading logarithm, l-loop improvement removes the next leading logarithm, etc. This property is also verified for related quantities such as the mass defined by the fall-off behavior of the fermion correlation function and the fermion-antifermion scattering amplitude in the singlet channel. As far as scaling is concerned, we observe that beyond tree improvement the β-function contains non-universal terms implying a difference between scaling and asymptotic scaling which increases with the order of improvement. Comparing for the dynamical mass the gain by supressing scaling violations versus the loss in asymptotic scale behavior, we argue that in a numerical approach the tree-improved action would yield the best estimate for the dynamical mass.

Spontaneous breaking of chiral symmetry in quantum chromodynamics

Abstract We prove that the chiral SU(2) × SU(2) symmetry of quantum chromodynamics with two massless quark flavours is spontaneously broken. The asymptotic freedom property of the theory is essential for the proof. The Goldstone theorem then implies that the theory contains a massless spin zero particle. We show that this Goldstone boson has the quantum numbers of the pion.

Weak coupling perturbative calculations of the Wilson loop for the standard action

Abstract Wilson loops of size m × n with m , n ≤6 are evaluated to second order in weak coupling perturbation theory. The results are compared with earlier estimates by Hattori and Kawai.

Order α 2 s massive quark contribution to the vacuum polarization of massles quarks

We calculate to order α2s in the QCD coupling the effect of massive quarks on the vacuum polarization of massless quarks both in a momentum subtraction scheme and in the (modified) minimal subtraction scheme. We also illustrate how decoupling of heavy quarks takes place in this context in the minimal subtraction scheme.

Lattice fermions at non-zero temperature and chemical potential

We study the free fermion gas at finite temperature and chemical potential in the lattice regularized version proposed by Hasenfratz and Karsch and by Kogut et al. Special emphasis is placed on the identification of the particle and antiparticle contributions to the partition function. In the case of naive fermions we show that the partition function no longer separates into particle-antiparticle contributions in the way familiar from the continuum formulation. The use of Wilson fermions, on the other hand, eliminates this unpleasant feature, and leads, after subtracting the vacuum contributions, to the familiar expressions for the average energy and charge densities.

Analyticity properties in q2 for moments of deep inelastic structure functions

Abstract The moments of deep inelastic structure functions introduced by Nachtmann and the familiar Cornwall-Norton moments are shown to be analytic functions of q 2 with a right-hand cut as the only physical sheet singularity. For the Nachtmann moments the analytic continuations to q 2 > 0 can again be expressed as projections of a virtual Compton amplitude. This representation is used to determine for q 2 > 0 the contribution of a single nucleon resonance as a first step towards an estimate in magnitude of these functions on the cut.