arXiv subjects
Publications and source records attributed to Urs M. Heller.
I review recent progress in the determination of the QCD phase diagram at finite temperature, in investigations of the nature of the transition or crossover from the hadronic phase to the quark-gluon plasma phase and in the determination of the equation of state. This talk will focus on results at zero chemical potential.
We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with 2+1 flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration. The calculations are performed on $28^3\times 96$ lattices with lattice spacing $a = 0.09$ fm and on $20^3\times 64$ lattices with lattice spacing $a = 0.12$ fm. We calculate the quark mass function, $M(q^2)$, and the wave-function renormalization function, $Z(q^2)$, for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both $Z(q^2)$ and $M(q^2)$ show little sensitivity to the ultraviolet cutoff.
We present an unquenched calculation of the quark propagator in Landau gauge with 2+1 flavors of dynamical quarks. We study the scaling behavior of the quark propagator in full QCD on two lattices with different lattice spacings and similar physical volume. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration.
For SU(2) lattice gauge theory with the fundamental-adjoint action an efficient heat-bath algorithm is not known so that one had to rely on Metropolis simulations supplemented by overrelaxation. Implementing a novel biased Metropolis-heat-bath algorithm for this model, we find improvement factors in the range 1.45 to 2.06 over conventionally optimized Metropolis simulations. If one optimizes further with respect to additional overrelaxation sweeps, the improvement factors are found in the range 1.3 to 1.8.
The effects of Gaussian quark-field smearing and analytic stout-link smearing on the correlations of gauge-invariant extended baryon operators are studied. Gaussian quark-field smearing substantially reduces contributions from the short wavelength modes of the theory, while stout-link smearing significantly reduces the noise from the stochastic evaluations. The use of gauge-link smearing is shown to be crucial for baryon operators constructed of covariantly-displaced quark fields. Preferred smearing parameters are determined for a lattice spacing a_s ~ 0.1 fm.
We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $ε$-regime of QCD. This correlation function has a unique and strong dependence on $F_π$, and thus provides an novel way to extract $F_π$ from lattice simulations. We test the method in a quenched lattice simulation with staggered fermions.
Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.
We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking, and its strong volume dependence indicates that the chiral condensate in the quenched theory is an ill-defined and divergent quantity. When we reweight configurations with the Dirac determinant to study the theory with N_f=1, we obtain a distribution of eigenvalues that is well-behaved and consistent with the theory of explicit symmetry breaking due to the anomaly.
We present an unquenched calculation of the quark propagator in Landau gauge with 2+1 flavors of dynamical quarks. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration. This quark action has been seen to have excellent rotational symmetry and scaling properties in the quenched quark propagator. Quenched and dynamical calculations are performed on a $20^3\times 64$ lattice with a nominal lattice spacing of $a = 0.125$ fm. The matched quenched and dynamical lattices allow us to investigate the relatively subtle sea quark effects, and even in the quenched case the physical volume of these lattices gives access to lower momenta than our previous study. We calculate the quark mass function and renormalization function for a variety of valence and sea quark masses.
The properties of the momentum space quark propagator in Landau gauge and Gribov copy free Laplacian gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are done on two lattices with different lattice spacing $a$ and the same physical volume. We have calculated the nonperturbative wave function renormalization function $Z(q)$ and the nonperturbative mass function $M(p)$ for a variety of bare quark masses and perform a simple linear extrapolation to the chiral limit. We focus on the comparison of the behavior of $Z(q)$ and $M(p)$ in the chiral limit in the two gauge fixing schemes as well as the behavior on two lattices with different lattice spacing $a$. We find that the mass functions $M(p)$ are very similar for the two gauges while the wave-function renormalization function $Z(q)$ is more strongly infrared suppressed in the Laplacian gauge than in the Landau gauge on the finer lattice. For Laplacian gauge, it seems that the finite $a$ error is large on the coarse lattice which has a lattice spacing $a$ of about 0.124 fm.
This talk will focus on recent results by the MILC collaboration from simulations of light hadrons in 2+1 flavor lattice QCD. We have achieved high precision results in the pseudoscalar sector, including masses and decay constants, plus quark masses and Gasser-Leutwyler parameters from well controlled chiral perturbation theory fits to our data. We also show spectroscopy results for vector mesons and baryons.
As a quantitative measure of localization, the inverse participation ratio of low lying Dirac eigenmodes and topological charge density is calculated on quenched lattices over a wide range of lattice spacings and volumes. Since different topological objects (instantons, vortices, monopoles, and artifacts) have different co-dimension, scaling analysis provides information on the amount of each present and their correlation with the localization of low lying eigenmodes.
We compute pseudoscalar meson masses and decay constants in partially quenched QCD with three dynamical flavors of improved staggered quarks. Fitting the lattice data to staggered chiral perturbation theory forms and extrapolating in quark mass and lattice spacing, we find: $f_π= 129.5 \pm 0.9 \pm 3.5$ MeV, $f_K = 156.6 \pm 1.0 \pm 3.6$ MeV, and $f_K/f_π= 1.210(4)(13)$. The value for $f_K/f_π$ implies $|V_{us}|=0.2219(26)$. We also obtain $m_u/m_d = 0.43(0)(1)(8)$, or, with more input on electromagnetic effects from the continuum, $m_u/m_d = 0.41(0)(1)(4)$. Using the one-loop perturbative mass renormalization, we determine $m_u$ and $m_d$ in the MSbar scheme.
Using lattice quantum chromodynamics (QCD) we perform an unquenched calculation of the gluon propagator in Landau gauge. We use configurations generated with the AsqTad quark action by the MILC collaboration for the dynamical quarks and compare the gluon propagator of quenched QCD (i.e., the pure Yang-Mills gluon propagator) with that of 2+1 flavor QCD. The effects of the dynamical quarks are clearly visible and lead to a significant reduction of the nonperturbative infrared enhancement relative to the quenched case.
We present a current summary of a program to study the quark propagator using lattice QCD. We use the Overlap and ``Asqtad'' quark actions on a number of lattice ensembles to assess systematic errors. We comment on the place of this work amongst studies of QCD Green's functions in other formulations. A preliminary calculation of the running quark mass is presented.
In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.
We compute pseudoscalar meson masses and decay constants using staggered quarks on lattices with three flavors of sea quarks and lattice spacings $\approx 0.12$ fm and $\approx 0.09$ fm. We fit partially quenched results to ``staggered chiral perturbation theory'' formulae, thereby taking into account the effects of taste-symmetry violations. Chiral logarithms are observed. From the fits we calculate $f_π$ and $f_K$, extract Gasser-Leutwyler parameters of the chiral Lagrangian, and (modulo rather large perturbative errors) find the light and strange quark masses.
We study the Glauber dynamics of simple spin systems to identify dynamical scenarios which may be of relevance for the deconfining phase transition in heavy ion collisions.