arXiv subjects
Publications and source records attributed to Jochen Heitger.
We report on a parallelized implementation of SSOR preconditioning for O(a) improved lattice QCD with Schrödinger functional boundary conditions. Numerical simulations in the quenched approximation at parameters in the light quark mass region demonstrate that a performance gain of a factor $\sim$ 1.5 over even-odd preconditioning can be achieved.
We review recent work by the ALPHA and UKQCD Collaborations where masses and matrix elements were computed in lattice QCD using Schrödinger functional boundary conditions and where the strange quark mass was determined in the quenched approximation. We emphasize the general concepts and our strategy for the computation of quark masses.
We determine the renormalization group invariant quark mass corresponding to the sum of the strange and the average light quark mass in the quenched approximation of QCD, using as essential input the mass of the K-mesons. In the continuum limit we find $(M_s + M_{light})/F_K=0.874(29)$, which includes systematic errors. Translating this non-perturbative result into the running quark masses in the $\msbar$-scheme at $μ=2 GeV$ and using the quark mass ratios from chiral perturbation theory, we obtain $\mbar_s(2 GeV)=97(4) MeV$. With the help of recent results by the CP-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced $F_K$ by the nucleon mass to set the scale. This is a typical ambiguity in the quenched approximation.
We explain how masses and matrix elements can be computed in lattice QCD using Schr"odinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schr"odinger functional technique turns out to be much more efficient than the known alternatives.
We present a scaling investigation of some correlation functions in $\Or(a)$ improved quenched lattice QCD. In particular, as one observable the renormalized PCAC quark mass is considered. Others are constructed such that they become the vector meson mass and the pseudoscalar meson decay constant when the volume is large. For the present discussion we remain in intermediate volume, $(0.75^3\times1.5) {fm}^4$ with Schrödinger functional boundary conditions. By fixing the `pion mass' and the spatial lattice size in units of the hadronic scale $r_0$, we simulated four lattices with resolutions ranging from 0.1 fm to 0.05 fm and performed the extrapolation to the continuum limit. The maximal scaling violation found in the improved theory is a $\sim$ 6 % effect at $a\simeq 0.1 fm$.
We present a scaling investigation of renormalized correlation functions in $\Or(a)$--improved quenched lattice QCD. As one observable the renormalized PCAC quark mass is considered, others are constructed such that they become the vector meson mass, and the pseudoscalar and vector meson decay constants in large volume. Presently, we remain in intermediate volume, $(0.75^3\times1.5) {fm}^4$, and study the approach to the continuum limit.
We study the finite-temperature electroweak phase transition by numerical simulations of the four-dimensional SU(2)-Higgs model on anisotropic lattices with temporal extension $L_t=2$. The physically interesting parameter region of Higgs masses near 80 GeV is reached, and recent results on some thermodynamic quantities are presented.
We study the continuum limit of the $2D$ U(1)--Higgs model with variable scalar field length, which is qualitatively different from the fixed length case. Our simulations concentrate on the scaling behaviour of the topological susceptibility, and an instanton-induced confinement mechanism of fractional charges is numerically confirmed.
We determine the interface tension of the finite-temperature electroweak phase transition in a numerical investigation of the SU(2)--Higgs model on a four-dimensional lattice with temporal extension $L_t=3$. In this simulation the chosen parameters correspond to a Higgs boson mass of about 16 GeV. As a result the interface tension shows only small scaling violations in comparison with previous studies for $L_t=2$ lattices. We also report on some experiences with autocorrelations in the applied Monte Carlo simulations of two-phase systems.
In three-dimensional systems of the Ising universality class the ratio of correlation length amplitudes for the high- and low-temperature phases is a universal quantity. Its field theoretic determination apart from the $ε$-expansion represents a gap in the existing literature. In this article we present a method, which allows to calculate this ratio by renormalized perturbation theory in the phases with unbroken and broken symmetry of a one-component $ϕ^4$-theory in fixed dimensions $D=3$. The results can be expressed as power series in the renormalized coupling constant of either of the two phases, and with the knowledge of their fixed point values numerical estimates are obtainable. These are given for the case of a two-loop calculation.