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Urs M. Heller

Publications and source records attributed to Urs M. Heller.

At least 73 records · Page 4Linked to original sources
arXiv1999

Topology and chiral symmetry in finite temperature QCD

We investigate the realization of chiral symmetry in the vicinity of the deconfinement transition in quenched QCD using overlap fermions. Via the index theorem obeyed by the overlap fermions, we gain insight into the behavior of topology at finite temperature. We find small eigenvalues, clearly separated from the bulk of the eigenvalues, and study the properties of their distribution. We compare the distribution with a model of a dilute gas of instantons and anti-instantons and find good agreement.

hep-lat↗
arXiv1999

Chiral Fermions on the Lattice

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator are reviewed.

hep-lat↗
arXiv1999

Thermodynamics with Dynamical Clover Fermions

We investigate the finite temperature behavior of nonperturbatively improved clover fermions on lattices with temporal extent N_t=4 and 6. Unfortunately in the gauge coupling range, where the clover coefficient has been determined nonperturbatively, the finite temperature crossover/transition occurs at heavy pseudoscalar masses and large pseudoscalar to vector meson mass ratios. However, on an N_t=6 lattice the thermal crossover for the improved fermions is much smoother than for unimproved Wilson fermions and no strange metastable behavior is observed.

hep-lat↗
arXiv1999

Quark spectra, topology and random matrix theory

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are tested for the first time.

hep-th↗
arXiv1999

Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensemble. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N_c), N_c=2, 3.

hep-lat↗
arXiv1999

Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson-Dirac operator in the range $0\le m\le 2$. We find that the spectrum has a gap for $0 < m \le m_1$ and that the spectral density at zero, $ρ(0;m)$, is non-zero for $m_1\le m\le 2$. We find that $m_1\to 0$ and, for $m \ne 0, ρ(0;m)\to 0$ (exponential in the lattice spacing) as one goes to the continuum limit. We also compute the topological susceptibility and the size distribution of the zero modes. The topological susceptibility scales well in the lattice spacing for both SU(2) and SU(3). The size distribution of the zero modes does not appear to show a peak at a physical scale.

hep-lat↗
arXiv1998

A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator

We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes and simplify our numerical computations. Details concerning the numerical implementation of the Overlap-Dirac operator are presented.

hep-lat↗
arXiv1998

Lattice Determination of Heavy-Light Decay Constants

We report on the MILC collaboration's calculation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios. Our central values come from the quenched approximation, but the quenching error is estimated from $N_F=2$ dynamical staggered lattices. We use Wilson light valence quarks and Wilson and static heavy quarks. We find, for example, $f_B=157 \pm 11 {}^{+25}_{-9} {}^{+23}_{-0} \MeV$, $f_{B_s}/f_B = 1.11 \pm 0.02 {}^{+0.04}_{-0.03} \pm 0.03$, $f_{D_s} = 210 \pm 9 {}^{+25}_{-9} {}^{+17}_{-1} \MeV$ and $f_{B}/f_{D_s} = 0.75 \pm 0.03 {}^{+0.04}_{-0.02} {}^{+0.08}_{-0.00}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively.

hep-ph↗
arXiv1998

Light hadron spectrum with Kogut-Susskind quarks

We made an extensive study of the light hadron spectrum using the Wilson gauge action and Kogut-Susskind quarks. Using both dynamical quarks and the quenched approximation, we determine hadron masses for five and four gauge couplings respectively, with at least five quark masses at each coupling. In the continuum limit, we find a significant difference between two flavors of dynamical quarks and the quenched approximation for a range of quark masses.

hep-lat↗
arXiv1998

Continuum limit of lattice QCD with staggered quarks in the quenched approximation - a critical role for the chiral extrapolation

We calculate the light quark spectrum of lattice QCD in the quenched approximation using Kogut-Susskind quarks. By combining results for different lattice spacings, several volumes and five quark masses, we are able to take the light quark mass, infinite volume, continuum limit. When we use non-linear chiral extrapolations, we find that the nucleon to rho mass ratio is 1.254 +- 0.018 +- 0.027, where the errors are statistical and systematic (within the quenched approximation), respectively. This should be compared with the experimental value of 1.22. Our results indicate that the error due to quenching is less than about 5%.

hep-lat↗
arXiv1998

Topological Susceptibility and Zero Mode Size in Lattice QCD

We use the overlap formalism to define a topological index on the lattice. We study the spectral flow of the hermitian Wilson-Dirac operator and identify zero crossings with topological objects. We determine the topological susceptibility and zero mode size distribution, and we comment on the stability of our results.

hep-lat↗
arXiv1998

Evidence for fractional topological charge in SU(2) pure Yang-Mills theory

We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge field configurations where the index of the hermitian Wilson-Dirac operator in the adjoint representation is not four times the index in the fundamental representation. This could imply a topological basis for the existence of degenerate vacua in supersymmetric Yang-Mills theories.

hep-lat↗
arXiv1998

Spectral flow, condensate and topology in lattice QCD

We study the spectral flow of the Wilson-Dirac operator H(m) with and without an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice gauge field ensembles in the range $0\le m \le 2$. We have used ensembles generated from the Wilson gauge action, an improved gauge action, and several two-flavor dynamical quark ensembles. Two regions in $m$ provide a generic characterization of the spectrum. In region I defined by $m\le m_1$, the spectrum has a gap. In region II defined by $m_1\le m \le 2$, the gap is closed. The level crossings in H(m) that occur in region II correspond to localized eigenmodes and the localization size decreases monotonically with the crossing point down to a size of about one lattice spacing. These small modes are unphysical, and we find the topological susceptibility is relatively stable in the part of region II where the small modes cross. We argue that the lack of a gap in region II is expected to persist in the infinite volume limit at any gauge coupling. The presence of a gap is important for the implementation of domain wall fermions.

hep-lat↗
arXiv1998

A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions

We study three practical implementations of the Overlap-Dirac operator $D_o= (1/2) [1 + γ_5ε(H_w)]$ in four dimensions. Two implementations are based on different representations of $ε(H_w)$ as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing $ε(H_w)$ using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator $H_o=γ_5 D_o$, we study its spectrum in a smooth SU(2) instanton background with the aim of comparing the three implementations of $D_o$. We also present some results in SU(2) gauge field backgrounds generated at $β=2.5$ on an $8^4$ lattice. Chiral properties have been numerically verified.

hep-lat↗
arXiv1998

Evidence for fractional topological charge in SU(2) pure Yang-Mills theory

We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge field configurations where the index of the hermitian Wilson-Dirac operator in the adjoint representation is not four times the index in the fundamental representation. This could imply a topological basis for the gluino condensate in supersymmetric Yang-Mills theories.

hep-lat↗
arXiv1998

Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions

We study the spectrum of $H(m)=γ_5 W(-m)$ with $W(m)$ being the Wilson-Dirac operator on the lattice with bare mass equal to $m$. The background gauge fields are generated using the SU(3) Wilson action at $β=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of $H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is massless in this whole region.

hep-lat↗
arXiv1998

The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds

We study the spectral flow of the hermitian Wilson-Dirac operator $\ham(m)$ as a function of $m$ in smooth SU(2) instanton backgrounds on the lattice. For a single instanton background with Dirichlet boundary conditions on $\ham(m)$, we find a level crossing in the spectral flow of $\ham(m)$, and we find the shape of the crossing mode at the crossing point to be in good agreement with the zero mode associated with the single instanton background. With anti-periodic boundary conditions on $\ham(m)$, we find that the instanton background in the singular gauge has the correct spectral flow but the one in regular gauge does not. We also investigate the spectral flows of two instanton and instanton-anti-instanton backgrounds.

hep-lat↗