Evidence for hard chiral logarithms in quenched lattice QCD

We present the first direct evidence that quenched QCD differs from full QCD in the chiral ($m_q \rightarrow 0$) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at $\beta = 6/g^2 = 6.0$. We measured the spectrum of light hadrons on $16^3 \times 64$, $24^3 \times 64$ and $32^3 \times 64$, using staggered quarks of masses $m_q=0.01$, $m_q=0.005$ and $m_q=0.0025$. The pion masses showed clear evidence for logarithmic violations of the PCAC relation $m_{\pi}^2 \propto m_q$, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate $\langle\bar{\psi}\psi\rangle$.Comment: 10 pages, 4 figures, uuencoded compressed postscript fil

Effects of spatial size, lattice doubling and source operator on the hadron spectrum with dynamical staggered quarks

We have extended our previous study of the lattice QCD spectrum with 2 flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the $\Delta$ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that $m_\pi^2 \propto m_q$, and $f_\pi$ is estimated. Use of undoubled lattices removes problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of $am_q=0.01$ when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, $am_q=0.025$. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.Comment: 30 pages PostScript fil

Hadron Spectrum in QCD with Valence Wilson Fermions and Dynamical Staggered Fermions at $6/g^2=5.6

We present an analysis of hadronic spectroscopy for Wilson valence quarks with dynamical staggered fermions at lattice coupling $6/g^2 = \beta=5.6$ at sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched approximation at $\beta=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We make comparisons with our previous results with dynamical staggered fermions at the same parameter values but on $16^4$ lattices doubled in the temporal direction.Comment: 32 page

A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the fermion action. The order parameter $$ was computed with the Hybrid Monte Carlo algorithm at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $\beta=4.0$ and 4.3, while we do not find parity-flavor breaking at $\beta=4.6$ and 5.0.Comment: 8 pages, 5 figures, Revised version as to be published in Phys.Rev.

QCD thermodynamics with two flavors of Wilson quarks at N_t=6

We report on a study of hadron thermodynamics with two flavors of Wilson quarks on 12^3x6 lattices. We have studied the crossover between the high and low temperature regimes for three values of the hopping parameter, kappa=0.16, 0.17, and 0.18. At each of these values of kappa we have carried out spectrum calculations on 12^3x24 lattices for two values of the gauge coupling in the vicinity of the crossover in order to set an energy scale for our thermodynamics calculations and to determine the critical value of the gauge coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we find coexistence between the high and low temperature regimes over 1,000 simulation time units indicating either that the equilibration time is extremely long or that there is a possibility of a first order phase transition. The pion mass is large at the crossover values of the gauge coupling, but the crossover curve has moved closer to the critical curve along which the pion and quark masses vanish, than it was on lattices with four time slices. In addition, values of the dimensionless quantity T_c/m_rho are in closer agreement with those for staggered quarks than was the case at N_t=4. (A POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)Comment: 24 page

Light Quark Masses from Lattice QCD

We present estimates of the masses of light quarks using lattice data. Our main results are based on a global analysis of all the published data for Wilson, Sheikholeslami-Wohlert (clover), and staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. We find that the values of masses with the various formulations agree after extrapolation to the continuum limit for the $n_f=0$ theory. Our best estimates, in the MSbar scheme at $\mu=2 GeV$, are \mbar=3.4 +- 0.4 +- 0.3 MeV and $m_s = 100 +- 21 +- 10 MeV$ in the quenched approximation. The $n_f=2$ results, \mbar = 2.7 +- 0.3 +- 0.3 MeV and $m_s = 68 +- 12 +- 7 MeV$, are preliminary. (A linear extrapolation in $n_f$ would further reduce these estimates for the physical case of three dynamical flavors.) These estimates are smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. The new results have a significant impact on the extraction of $\epsilon'/\epsilon$ from the Standard Model. Using the same lattice data we estimate the quark condensate using the Gell-Mann-Oakes-Renner relation. Again the three formulations give consistent results after extrapolation to $a=0$, and the value turns out to be correspondingly larger, roughly preserving m_s \vev{\bar \psi \psi}.Comment: 32 pages. Package submitted in uufiles format: unpack and tex paper.tex. Modified "axis" source for figures also included. Latex2e document. Uncomment hyperref if available. This is the final published versio

Properties of the a1 Meson from Lattice QCD

We determine the mass and decay constant of the $a_1$ meson using Monte Carlo simulation of lattice QCD. We find $M_{a_1} = 1250 \pm 80$ MeV and $f_{a_1} = 0.30 \pm 0.03 ~({\rm GeV})^2$, in good agreement with experiment.Comment: 9 page uu-encoded compressed postscript file. version appearing in Phys. Rev. Lett. 74 (1995) 459

Dynamical Wilson fermions and the problem of the chiral limit in compact lattice QED

We compare the approach to the chiral transition line ~\kappa_c(\bt)~ in quenched and full compact lattice QED with Wilson fermions within the confinement phase, especially in the pseudoscalar sector of the theory. We show that in the strong coupling limit ($\beta =0$) the quenched theory is a good approximation to the full one, in contrast to the case of $\beta =0.8$. At the larger $\beta$-value the transition in the full theory is inconsistent with the zero--mass limit of the pseudoscalar particle, thus prohibiting the definition of a chiral limit.Comment: 13 pages LaTeX (epsf), all figures include

Spontaneous Flavor and Parity Breaking with Wilson Fermions

We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $\Delta m_0 \sim a^3$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a$. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.Comment: 22 pages, LaTeX, 5 figures (added several references and a comment