Staggered Fermion Action Research Articles

B DECAYS ON THE LATTICE AND RESULTS FOR PHENOMENOLOGY

Lattice Monte Carlo simulations now include the effects of 2 light sea quarks and 1 strange sea quark through the use of an improved staggered fermion action. Consequently, results important to phenomenology are free of the approximate 10% errors inherent in the quenched approximation. This talk reports on calculations of the B and Bs, decay constants and B → πℓν form factors. Accurate determinations of these quantities will lead to tighter constraints on CKM matrix elements.

Topology and Staggered Fermion Action Improvement

It is conventional wisdom that staggered fermions do not feel gauge field topology. However, the response of staggered fermion eigenmodes to the topology of the gauge field can depend quite sensitively on the way in which the staggered fermion action is improved. We study this issue using a variety of improved staggered quark actions. We observe that the separation between the ``would be'' zero modes and the non-chiral modes increases with the level of improvement. This enables the ``zero modes'' to be identified unambiguously. The distribution of the remaining non-chiral modes is compared with the predictions of Random Matrix Theory. Satisfactory agreement is obtained.

On quark mass and lattice spacing dependence of the singlet free energies with improved fermions

We study scaling of the singlet free energies with quark mass and lattice spacing. The theory is three flavor QCD with degenerate quark masses using N τ = 4 and 6 lattices with Asqtad staggered fermion action.

Free energy of a static quark-antiquark pair and the renormalized Polyakov loop in three flavor QCD

We study the free energy of a static quark-antiquark ($Q\overline{Q}$) pair at finite temperature in three flavor QCD with degenerate quark masses using ${N}_{\ensuremath{\tau}}=4$ and $6$ lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.

Scaling test of quenched hypercubic smeared staggered fermions

Abstract We investigate the scaling behavior of the hypercubic smeared (HYP) staggered fermion action in the quenched limit at lattice spacings a = 0.165, 0.135 and 0.095fm with pion masses as low as 250MeV. Even on the coarsest lattice we find no scaling violations for hadronic observables suggesting that HYP smearing removes most lattice artifacts.

DIRAC–KÄHLER FERMION FROM CLIFFORD PRODUCT WITH NONCOMMUTATIVE DIFFERENTIAL FORM ON A LATTICE

We formulate Dirac–Kähler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac–Kähler action requires to choose the lattice structure having both orientabilities on a link. The Kogut–Susskind fermion and the staggered fermion actions are derived directly from the Dirac–Kähler fermion formulated by the Clifford product. The lattice QCD action with Dirac–Kähler matter fermion is also derived via an inner product defined by the Clifford product.

The deconfining phase transition in full QCD with two dynamical flavors

We investigate the deconfining phase transition in SU(3) pure gauge theory and in full QCD with two flavors of staggered fermions. The phase transition is detected by measuring the free energy in presence of an abelian monopole background field. In the pure gauge case our finite size scaling analysis is in agreement with the well known presence of a weak first order phase transition. In the case of 2 flavors full QCD we find, using the standard pure gauge and staggered fermion actions, that the phase transition is consistent with weak first order, contrary to the expectation of a crossover for not too large quark masses and in agreement with results obtained by the Pisa group.

Self-energy of improved staggered quarks

We calculate the fermion self-energy at $O({\ensuremath{\alpha}}_{s})$ for the Symanzik improved staggered fermion action used in recent lattice simulations by the MILC Collaboration. We demonstrate that the algebraic approach to lattice perturbation theory, suggested by us recently, is a powerful tool also for improved lattice actions.

Perturbative improvement of staggered fermions using fat links

We study possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness and equivalence. As a result of these theorems, we show that, at one loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation.

The chiral critical point in 3-flavour QCD

We determine the second order endpoint of the line of first order phase transitions, which occur in the light quark mass regime of 3-flavour QCD at finite temperature, and analyze universal properties of this chiral critical point. A detailed analysis of Binder cumulants and the joint probability distributions of energy like and ordering-field like observables confirms that the chiral critical point belongs to the universality class of the 3d Ising model. From a calculation with improved gauge and staggered fermion actions we estimate that the transition is first order for pseudo-scalar meson masses less than about 200 MeV.

Heavy-light physics using NRQCD-staggered actions

One leading source of uncertainty in the lattice computation of semi-leptonic form factors in B decay, and to a lesser extent B meson decay constants, comes from the extrapolation of the light quark mass to the physical up/down mass. This talk presents first explorations of simulating the light quark with staggered fermion actions, which are free of the spurious zero modes that effect Wilson-like Dirac operators and are less costly. Methods for fitting to Euclidean-time NRQCD-staggered meson propagators are discussed, and some preliminary spectrum results are presented.

The chiral critical point in 3-flavour QCD

We determine the second order endpoint of the line of first order phase transitions, which occur in the light quark mass regime of 3-flavour QCD at finite temperature, and analyze universal properties of this chiral critical point. A detailed analysis of Binder cumulants and the joint probability distributions of energy like and ordering-field like observables confirms that the chiral critical point belongs to the universality class of the three-dimensional Ising model. From a calculation with improved gauge and staggered fermion actions we estimate that the transition is first order for pseudo-scalar meson masses less than about 200 MeV.

Topological susceptibility on dynamical staggered fermion configurations

The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends quadratically on the pion mass, approaching zero in the chiral limit. Lattice calculations have difficulty reproducing this behavior. In this paper we study the topological susceptibility on dynamical staggered fermion configurations. Our results indicate that the lattice spacing has to be small, around a~0.1fm for thin link staggered fermion actions to show the expected chiral behavior. Our preliminary result indicates that fat link fermions, on the other hand, reproduce the theoretical expectations even on lattices with a~0.17fm. We argue that this is due to the improved flavor symmetry of fat link fermionic actions.

Flavor and quark mass dependence of QCD thermodynamics

We calculate the transition temperature in 2 and 3-flavor QCD using improved gauge and staggered fermion actions on lattices with temporal extent N τ = 4. We find T c = 173 (8) MeV and 154 (8) MeV for n f = 2 and 3, respectively. In the case of 3-flavor QCD we present evidence that the chiral critical point, i.e. the second order endpoint of the line of first order chiral phase transitions, belongs to the universality class of the 3d Ising model.

Quark loop effects with an improved staggered fermion action

We have been studying effects of dynamical quarks on various hadronic observables, using our recently formulated improvement for staggered fermions. To illustrate improvement, we show that the light hadron spectrum in the quenched approximation gives remarkably good scaling. We highlight three new results: (1) We find no apparent quark loop effects in the Edinburgh plot with 2+1 flavors of dynamical quarks at a = 0.14 fm. (2) We show that dynamical quarks modify the shape of the heavy quark potential. (3) We present results hinting at meson decay effects in light hadron spectroscopy.

Improved staggered fermion actions for QCD thermodynamics

We analyze the cutoff dependence of the fermion contribution to the finite temperature free energy density in ${O(g}^{2})$ lattice perturbation theory for several improved staggered fermion actions. Cutoff effects are drastically reduced for the Naik action and an action with improved rotational symmetry of the quark propagator. We show that improvement of the rotational symmetry at ${O(g}^{2})$ further reduces cutoff effects in thermodynamic observables. We also show that the introduction of fat links does not have a significant influence on cutoff distortions at ${O(g}^{2}).$

Improvement, dynamical fermions, and heavy quark screening in QCD 3

First results from simulations of improved actions for both gauge fields and staggered fermion fields in three dimensional QCD are presented. This work provides insight into some issues of relevance to lattice theories in four dimensions. In particular, the renormalization of the bare lattice coupling is dramatically reduced when the tree-level O( a 2) improved action is used. Naik improvement of the staggered fermion action produces little reduction in scaling violations of the rho meson mass. String breaking in the heavy quark potential in the unquenched theory is also clearly resolved, using Wilson loops to bound the ground state energy.

Staggered fermion actions with improved rotational invariance

We introduce a class of improved actions for staggered fermions which to O ( p 4) and O ( p 6), respectively, lead to rotationally invariant propagators. We discuss the resulting reduction of flavour symmetry breaking in the meson spectrum and comment on the improvement in the calculation of thermodynamic observables.

On QCD thermodynamics with improved actions

We discuss recent advances in the calculation of thermodynamic observables using improved actions. In particular, we discuss the calculation of the equation of state of the SU(3) gauge theory, the critical temperature in units of the string tension, the surface tension and the latent heat at the deconfinement transition. We also present first results from a calculation of the equation of state for four-flavour QCD using an O(a^2) improved staggered fermion action and discuss possible further improvements of the staggered fermion action.

Staggered fermions and their O( a) improvements

Expanding upon the arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order a terms in the staggered fermion action. We propose a general program to improve fermion operators to remove O( a) corrections from their matrix elements, and demonstrate this program for the examples of matrix elements of fermion bilinears and B K . We also determine the additional operators which must be added to improve the standard staggered fermion currents.