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Karl Jansen

Publications and source records attributed to Karl Jansen.

322 records · Page 18Linked to original sources
arXiv1995

Non-perturbative renormalization of lattice QCD at all scales

A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization constant, the running coupling at zero quark masses and the scale evolution of the renormalized axial density. The non-perturbative calculation of O(a) correction terms (as they appear in Symanzik's improvement programme) is another important field of application.

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arXiv1995

Kramers equation algorithm for simulations of QCD with two flavors of Wilson fermions and gauge group SU(2)

We compare the Hybrid Monte Carlo (HMC) and the Kramers equation algorithms for simulations of QCD with two flavors of dynamical Wilson fermions and gauge group $SU(2)$. The results for the performance of both algorithms are obtained on $6^312$, $12^4$ and $16^4$ lattices at a pion to $ρ$ meson mass ratio of $m_π/m_ρ\approx 0.9$. We find that the Kramers equation algorithm gives an equally good performance as the HMC algorithm. We demonstrate that the classical equations of motion used in these algorithms lack reversibility in practical simulations and behave like those of a chaotic dynamical system with a Liapunov exponent $ν\approx 0.75$.

hep-lat↗
arXiv1994

Domain Wall Fermions and Chiral Gauge Theories

We review the status of the domain wall fermion approach to construct chiral gauge theories on the lattice. In this model an extra, fifth dimension is added and our 4-dimensional world lives on a domainwall induced by a soliton shaped mass defect that depends on the extra dimension only. We demonstrate that the domain wall model gives the correct anomaly structure when external gauge fields are used. We discuss two ways of adding dynamical gauge fields aiming at a lattice regularized chiral gauge theory. An approach is presented to keep the lattice infinite by regarding the fifth direction as the time-axis of a 4-dimensional Hamiltonian. Finally, a prospect to use domain wall fermions for simulating QCD is given.

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arXiv1994

A Heavy Higgs Particle in the TeV Mass Range ?

The first simulation results are presented on Higgs mass calculations in the spontaneously broken phase of the Higgs sector in the minimal Standard Model with higher derivative regulator. A heavy Higgs particle is found in the TeV mass range in the presence of a complex conjugate ghost pair at higher energies. The ghost pair evades easy experimental detection and a nonperturbative reinterpretation of the triviality Higgs mass bound becomes necessary.

hep-lat↗
arXiv1993

Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue that in an anomaly free model these extra modes would decouple if our model possesses a so-called strong coupling symmetric phase. However, our numerical results indicate that such a phase most probably does not exist. ---- Note: 9 Postscript figures are appended as uuencoded compressed tar file.

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arXiv1993

The Higgs Model with a Complex Ghost Pair

A higher derivative term is introduced in the kinetic energy of the Higgs Lagrangian in the minimal Standard Model. A logically consistent and {\it finite} field theory is obtained when some excitations of the Higgs field are quantized with indefinite metric in the Hilbert space. The Landau ghost phenomenon of the conventional triviality problem is replaced by the state vectors of a complex ghost pair at a finite mass scale with observable physical consequences. It is shown that the ghost states exhibit unusual resonance properties and correspond to a complex conjugate pair of Pauli-Villars regulator masses in the euclidean path integral formulation of the theory. An argument is given that microscopic acausality effects associated with the ghost pair remain undetectable in scattering processes with realistic wave packects, and the S-matrix should exhibit unitarity in the observable sector of the Hilbert space. Part One of Extended UCSD-PTH 92-40

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arXiv1993

Strongly Interacting Higgs Sector in the Minimal Standard Model?

The triviality Higgs mass bound is studied with a higher derivative regulator in the spontaneously broken phase of the four dimensional O(4) symmetric scalar field theory with quartic self-interaction. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the Higgs mass bound in continuum space-time. In a large-N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs sector in the TeV region with negligible dependence on regulator parameters. When the higher derivative regulator mass is brought close to the Higgs mass the model requires a more elaborate analysis of complex ghost states in scattering amplitudes. Part Two of Extended UCSD-PTH 92-40

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arXiv1992

Strongly Interacting Higgs Sector in the Minimal Standard Model?

The triviality Higgs mass bound is studied {\it without} lattice regulator in the spontaneously broken phase of the four dimensional O(4) symmetric scalar field theory with quartic self-interaction. A higher derivative term is introduced in the kinetic energy of the Lagrangian to keep quantum fluctuations finite while preserving all the symmetries of the model. When viewed as a {\it finite} field theory in continuum space-time, some excitations of the Higgs field have to be quantized with indefinite metric in the Hilbert space. It is shown that the associated ghost particles, which exhibit unusual resonance properties, correspond to a complex conjugate pair of Pauli-Villars regulator masses in the euclidean path integral formulation. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the triviality Higgs mass bound without lattice artifacts. In a large-N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs

hep-lat↗
arXiv1992

Chiral Fermions, Anomalies and Chern-Simons Currents on the Lattice

I discuss the zeromode spectrum of lattice chiral fermions in the domain wall model suggested recently. In particular I give the critical momenta where the fermions cease to be chiral and show that the spectrum is directly related to the behaviour of the Chern-Simons current on the lattice. First results for the domain wall model on the finite lattice indicate that the relevant features of the model in the infinite system survive for the finite lattice.

hep-lat↗
arXiv1992

The Finite Temperature Phase Diagram of a U(1) Higgs-Yukawa Model

The finite temperature phase diagram of a U(1) Higgs-Yukawa model at a finite value of the scalar self coupling $λ$ is investigated by means of a large-$N_f$ calculation and numerical simulations. The phase diagram is similar to the one at zero temperature and shows a ferromagnetic, two symmetric and an antiferromagnetic phase. However, the phase transition lines are shifted to larger values of the Yukawa coupling demonstrating the occurence of the finite temperature symmetry restoration.

hep-lat↗
arXiv1992

Critical Momenta of Lattice Chiral Fermions

We determine the critical momenta for chiral fermions in the domain wall model recently suggested by Kaplan. For a wide range of domain wall masses $m$ and Wilson couplings $r$ we explicitly exhibit the regions in momentum space where the fermions are chiral. We compare the critical momenta for the infinitely large system with those obtained on a finite lattice.

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arXiv1992

Chern-Simons Currents and Chiral Fermions on the Lattice

We compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$ dimensional lattice, making use of a topological interpretation of the momentum space fermion propagator as a map from the torus to the sphere, $T^{d}\to S^{d}$. These mappings are shown to fall in different homotopy classes depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the Wilson coupling. As a result, the induced Chern-Simons term changes discontinuously at $d+1$ different values for $m$, unlike in the continuum. This behavior is exactly what is required by the peculiar spectrum found for a recently proposed model of chiral lattice fermions as zeromodes bound to a domain wall.

hep-lat↗
arXiv1992

Chiral Fermions and Anomalies on a Finite Lattice

A recent proposal by Kaplan for a chiral gauge theory on the lattice is tested with background gauge fields. The spectrum of the finite lattice Hamiltonian is calculated and the existence of a chiral fermion is demonstrated. Lattice doublers are found to decouple. The flavor anomalies, which are in agreement with the continuum anomaly relation, are obeserved on a finite lattice. Non-trivial anomaly cancellation is observed in a chiral gauge current.

hep-lat↗
arXiv1992

Tunneling and Energy Splitting in Ising Models

The energy splitting $E_{0a}$ in two and four dimensional Ising models is measured in a cylindrical geometry on finite lattices. By comparing to exact results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be extracted very reliably from Monte Carlo calculations in practice. In four dimensions we compare the measured $E_{0a}$ with two different theoretical predictions on the finite size behavior of the energy splitting. We find that our numerical data are in favor of the predictions based on the semiclassical dilute instanton gas approximation.

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