arXiv subjects
Publications and source records attributed to D. Toussaint.
We repeat our original simulations of the hybrid meson spectrum using the clover action, as a check on lattice artifacts. Our results for the 1-+ masses do not substantially change. We present preliminary results for the wave function of the 1-+ state in Coulomb gauge.
We present an update on the MILC Collaboration's light hadron spectrum calculation with two flavors of dynamical, staggered quarks. We present extrapolations of the nucleon to rho mass ratio to the continuum limit for fixed values of the pi to rho mass ratio including the physical one.
Quantum chromodynamics with two zero mass flavors is expected to exhibit a phase transition with O(4) critical behavior. Fixing the universality class is important for phenomenology and for facilitating the extrapolation of simulation data to physical quark mass values. At Lattice '96 the Tsukuba and Bielefeld groups reported results from new simulations with dynamical staggered quarks at $N_t = 4$, which suggested a departure from the expected critical behavior. We report observations of similar deviations and discuss efforts in progress to understand this phenomenon.
MILC collaboration results for \fB, \fBs, \fD, \fDs and their ratios are presented. These results are still preliminary, but the analysis is close to being completed. Sources of systematic error, both within the quenched approximation and from quenching itself, are estimated. We find, for example, $f_B=153\pm 10 {}^{+36}_{-13} {}^{+13}_{-0} MeV$, and $f_{B_s}/f_B = 1.10 \pm 0.02 {}^{+0.05}_{-0.03} {}^{+0.03}_{-0.02}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively. The extrapolation to the continuum and the chiral extrapolation are the largest sources of error. Present central values are based on linear chiral extrapolations; a shift to quadratic extrapolations would raise $f_B$ by $\approx20$ MeV and make the error within the quenched approximation more symmetric.
We use simulations of heavy quark effective field theory to calculate the Isgur-Wise function, and we demonstrate the feasibility of calculating the matrix element for the $B \to π+ \leptons$ decay in the lattice heavy quark effective theory (HQET).
The MILC collaboration computation of heavy-light decay constants is described. Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios are presented. These results are still preliminary, but the analysis is close to being completed. Sources of systematic error, both within the quenched approximation and from quenching itself, are estimated, although the latter estimate is rather crude. A sample of our results is: $f_B=153 \pm 10 {}^{+36}_{-13} {}^{+13}_{-0} MeV$, $f_{B_s}/f_B = 1.10 \pm 0.02 {}^{+0.05}_{-0.03} {}^{+0.03}_{-0.02}$, and $f_{B}/f_{D_s} = 0.76 \pm 0.03 {}^{+0.07}_{-0.04} {}^{+0.02}_{-0.01}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively. The largest source of error comes from the extrapolation to the continuum. The second largest source is the chiral extrapolation. At present, the central values are based on linear chiral extrapolations; a shift to quadratic extrapolations would for example raise $f_B$ by $\approx 20$ MeV and thereby make the error within the quenched approximation more symmetric.
We calculate the two flavor equation of state for QCD on lattices with lattice spacing a=(6T)^{-1} and find that cutoff effects are substantially reduced compared to an earlier study using a=(4T)^{-1}. However, it is likely that significant cutoff effects remain. We fit the lattice data to expected forms of the free energy density for a second order phase transition at zero-quark-mass, which allows us to extrapolate the equation of state to m_q=0 and to extract the speed of sound. We find that the equation of state depends weakly on the quark mass for small quark mass.
We have extended our earlier simulations of the high temperature behaviour of lattice QCD with two light flavours of staggered quarks on a $16^3 \times 8$ lattice to lower quark mass (m_q=0.00625). The transition from hadronic matter to a quark-gluon plasma is observed at $6/g^2=5.49(2)$ corresponding to a temperature of $T_c \approx 140$MeV. We present measurements of observables which probe the nature of the quark-gluon plasma and serve to distinguish it from hadronic matter. Although the transition is quite abrupt, we have seen no indications that it is first order.
Sigma models for the high temperature phase transition in quantum chromodynamics (QCD) suggest that at high temperature the SU(N_f) x SU(N_f) chiral symmetry becomes exact, but the anomalous axial U(1) symmetry need not be restored. In numerical lattice simulations, traditional methods for detecting symmetry restoration have sought multiplets in the screening mass spectrum. However, these methods were imprecise and the results, so far, incomplete. With improved statistics and methodology, we are now able to offer evidence for a restoration of the SU(2) x SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move; this is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover for any nonzero density at which we simulated, and that at low enough temperature chiral symmetry remains broken at all densities.
We describe the current status of the MILC collaboration computation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios. Progress over the past year includes: better statistics and plateaus at $β=6.52$ (quenched), $β=5.6$ ($N_F=2$) and $β=5.445$ ($N_F=2$), new runs with a wide range of dynamical quark masses at $β=5.5$ ($N_F=2$), an estimate of the systematic errors due to the chiral extrapolation, and an improved analysis which consistently takes into account both the correlations in the data at every stage and the systematic effects due to changing fitting ranges.
As part of a larger project to estimate the fB decay constant, we are recalculating fB_static using a variational smearing method in an effort to improve accuracy. Preliminary results for the static B_B parameter and HQET two point functions are also presented.
We conclude our analysis of the N_t=6 equation of state for two flavor QCD, first described at last year's conference. We have obtained new runs at am_q=0.025 and improved runs at am_q=0.0125. The results are extrapolated to m_q=0, and we extract the speed of sound as well. We also present evidence for a restoration of the SU(2) X SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.
We improve the calculation of the equation of state for two flavor QCD by simulating on $N_t=6$ lattices at appropriate values of the couplings for the deconfinement/chiral symmetry restoration crossover. For $am_q=0.0125$ the energy density rises rapidly to approximately 1 ${\rm GeV/fm^3}$ just after the crossover($m_π/m_ρ\approx 0.4$ at this point). Comparing with our previous result for $N_t=4$~\cite{eos}, we find large finite $N_t$ corrections as expected from free field theory on finite lattices. We also provide formulae for extracting the speed of sound from the measured quantities.
Previous work at $6/g^2=5.7$ with quenched staggered quarks is extended with new calculations at 5.85 and 6.15 on lattices up to $32^3\times 64$. These calculations allow a more detailed study of extrapolation in quark mass, finite volume and lattice spacing than has heretofore been possible. We discuss how closely the quenched spectrum approaches that of the real world.
We present new results in an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover, an important indicator of continuum scaling, a determination of the induced baryon charge and baryon susceptibility, used to study the dissolution of hadrons at the crossover, the scalar susceptibility, a signal for the appearance of soft modes, and the chiral order parameter, used to test models of critical behavior.
Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios are presented. High statistics quenched runs at $β=5.7$, $5.85$, $6.0$, and $6.3$, plus a run still in progress at $β=6.52$ make possible a preliminary extrapolation to the continuum. The data allows good control of all systematic errors except for quenching, although not all of the error estimates have been finalized. Results from configurations which include effects of dynamical quarks show a significant deviation from the quenched results and make possible a crude estimate of the quenching error.
Preliminary results from the MILC collaboration for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios are presented. We compute in the quenched approximation at $β=6.3$, 6.0 and 5.7 with Wilson light quarks and static and Wilson heavy quarks. We attempt to quantify all systematic errors other than quenching, and have a first indication of the size of quenching errors.