Karl Jansen

Locality properties of Neuberger's lattice Dirac operator

Abstract The gauge covariant lattice Dirac operator D which has recently been proposed by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral symmetry. The operator also avoids a doubling of fermion species, but its locality properties are not obvious. We now prove that D is local (with exponentially decaying tails) if the gauge field is sufficiently smooth at the scale of the cutoff. Further analytic and numerical studies moreover suggest that the locality of the operator is in fact guaranteed under far more general conditions.

O(a) improvement of lattice QCD with two flavors of Wilson quarks

Abstract We consider O)(a) improvement for two flavor lattice QCD. The improvement term in the action is computed non-perturbatively for a large range of the bare coupling. The position of the critical line and higher order lattice artifacts remaining after improvement are estimated. We also discuss the behavior of the HMC algorithm in our simulations.

The equivalence of the top quark condensate and the elementary Higgs field

Abstract Several recent works suggested to replace the fundamental Higgs boson by a top quark condensate in analogy with the Nambu-Jona-Lasinio (NJL) mechanism. We show that the field theoretically correct replacement is a generalized NJL model with the minimal choice of three independent interaction terms in the lagrangian. We demonstrate in the large- N color limit that the physics of this model is fully equivalent to the corresponding simplified Standard Model where the Higgs boson is represented by an elementary scalar field with the usual Yukawa- and self-interactions. The generalized NJL mechanism does not lead to new physical predictions or constraints and the complete parameter range of the simplified Standard Model is recovered. Since there exists a simple mapping between the couplings of these two models, it is difficult to give physical significance to notions like composite versus fundamental, or dynamical symmetry breaking in this scheme. We also present some new numerical results on the relevant phase diagrams.

Speeding up lattice QCD simulations with clover improved Wilson fermions

Abstract We apply a recent proposal to speed up the hybrid Monte Carlo simulation of systems with dynamical fermions to two flavour QCD with clover-improvement. The basic idea of our proposal is to split the fermion matrix into two factors with a reduced condition number each. In the effective action, for both factors a pseudo-fermion field is introduced. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.

A polynomial hybrid Monte Carlo algorithm

Abstract We present a simulation algorithm for dynamical fermions that combines the multiboson technique with the hybrid Monte Carlo algorithm. We find that the algorithm gives a substantial gain over the standard methods in practical simulations. We point out the ability of the algorithm to treat fermion zero modes in a clean and controllable manner.

Simulating the electroweak phase transition in the SU(2) Higgs model

Abstract Numerical simulations are performed to study the finite temperature phase transition in the SU (2) Higgs model on the lattice. In the presently investigated range of the Higgs boson mass, below 50 GeV, the phase transition turns out to be of first order and its strength is rapidly decreasing with increasing Higgs boson mass. In order to control the systematic errors, we also perform studies of scaling violations and of finite volume effects.

Finite size scaling of the quark condensate in quenched lattice QCD

Abstract We confront the finite volume and small quark mass behaviour of the scalar condensate, determined numerically in quenched lattice QCD using Neuberger fermions, with predictions of quenched chiral perturbation theory. We find that quenched chiral perturbation theory describes the numerical data well, allowing us to extract the infinite volume, chiral limit scalar condensate, up to a multiplicative renormalization constant.

Chern-Simons currents and chiral fermions on the lattice

Abstract We compute the Chern-Simons current induced by lattice fermions on a d(=2n+1)-dimensional lattice, using a topological interpretation of the fermion propagator as a map from the torus to the sphere, Td→Sd. Our techniques clarify the dependence of the current on short-distance physics. We show explicitly that for Wilson fermions it changes discontinuously at d+1 different values for the mass m. This result is relevant for a recently proposed model of chiral fermions as zeromodes bound to a domain wall.

Finite-size Scaling of Meson Propagators

Abstract Using quenched chiral perturbation theory we compute meson correlation functions at finite volume and fixed gauge field topology. We also present the corresponding analytical predictions for the unquenched theory at fixed gauge field topology. These results can be used to measure the low-energy parameters of the chiral Lagrangian from lattice simulations in volumes much smaller than one pion Compton wavelength.

Low-lying baryon spectrum with two dynamical twisted mass fermions

The masses of the low-lying baryons are evaluated using two degenerate flavors of twisted mass sea quarks corresponding to pseudoscalar masses in the range of about 270\char21{}500 MeV. The strange valence quark mass is tuned to reproduce the mass of the kaon in the physical limit. The tree-level Symanzik improved gauge action is employed. We use lattices of spatial size 2.1 and 2.7 fm at two values of the lattice spacing with